LMFDB - Embedded newform 70.3.f.a.57.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,3,Mod(43,70)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("70.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	70.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.90736185052$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 49 $ x^4 + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			57.2
Root			$1.87083 - 1.87083i$ of defining polynomial
Character	$\chi$	$=$	70.57
Dual form			70.3.f.a.43.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(2.87083 - 2.87083i) q^{3} +2.00000i q^{4} +(4.87083 + 1.12917i) q^{5} -5.74166 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -7.48331i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(2.87083 - 2.87083i) q^{3} +2.00000i q^{4} +(4.87083 + 1.12917i) q^{5} -5.74166 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -7.48331i q^{9} +(-3.74166 - 6.00000i) q^{10} -13.9666 q^{11} +(5.74166 + 5.74166i) q^{12} +(6.61249 - 6.61249i) q^{13} +3.74166i q^{14} +(17.2250 - 10.7417i) q^{15} -4.00000 q^{16} +(8.09580 + 8.09580i) q^{17} +(-7.48331 + 7.48331i) q^{18} +14.2583i q^{19} +(-2.25834 + 9.74166i) q^{20} -10.7417 q^{21} +(13.9666 + 13.9666i) q^{22} +(-28.7083 + 28.7083i) q^{23} -11.4833i q^{24} +(22.4499 + 11.0000i) q^{25} -13.2250 q^{26} +(4.35414 + 4.35414i) q^{27} +(3.74166 - 3.74166i) q^{28} -20.0334i q^{29} +(-27.9666 - 6.48331i) q^{30} +0.775028 q^{31} +(4.00000 + 4.00000i) q^{32} +(-40.0958 + 40.0958i) q^{33} -16.1916i q^{34} +(-7.00000 - 11.2250i) q^{35} +14.9666 q^{36} +(37.2250 + 37.2250i) q^{37} +(14.2583 - 14.2583i) q^{38} -37.9666i q^{39} +(12.0000 - 7.48331i) q^{40} -29.6749 q^{41} +(10.7417 + 10.7417i) q^{42} +(54.4833 - 54.4833i) q^{43} -27.9333i q^{44} +(8.44994 - 36.4499i) q^{45} +57.4166 q^{46} +(-64.0291 - 64.0291i) q^{47} +(-11.4833 + 11.4833i) q^{48} +7.00000i q^{49} +(-11.4499 - 33.4499i) q^{50} +46.4833 q^{51} +(13.2250 + 13.2250i) q^{52} +(-17.7083 + 17.7083i) q^{53} -8.70829i q^{54} +(-68.0291 - 15.7707i) q^{55} -7.48331 q^{56} +(40.9333 + 40.9333i) q^{57} +(-20.0334 + 20.0334i) q^{58} +60.1249i q^{59} +(21.4833 + 34.4499i) q^{60} -86.9666 q^{61} +(-0.775028 - 0.775028i) q^{62} +(-14.0000 + 14.0000i) q^{63} -8.00000i q^{64} +(39.6749 - 24.7417i) q^{65} +80.1916 q^{66} +(-41.7083 - 41.7083i) q^{67} +(-16.1916 + 16.1916i) q^{68} +164.833i q^{69} +(-4.22497 + 18.2250i) q^{70} -47.4833 q^{71} +(-14.9666 - 14.9666i) q^{72} +(34.3832 - 34.3832i) q^{73} -74.4499i q^{74} +(96.0291 - 32.8708i) q^{75} -28.5167 q^{76} +(26.1292 + 26.1292i) q^{77} +(-37.9666 + 37.9666i) q^{78} -9.13348i q^{79} +(-19.4833 - 4.51669i) q^{80} +92.3498 q^{81} +(29.6749 + 29.6749i) q^{82} +(78.9666 - 78.9666i) q^{83} -21.4833i q^{84} +(30.2917 + 48.5748i) q^{85} -108.967 q^{86} +(-57.5124 - 57.5124i) q^{87} +(-27.9333 + 27.9333i) q^{88} +80.0000i q^{89} +(-44.8999 + 28.0000i) q^{90} -24.7417 q^{91} +(-57.4166 - 57.4166i) q^{92} +(2.22497 - 2.22497i) q^{93} +128.058i q^{94} +(-16.1001 + 69.4499i) q^{95} +22.9666 q^{96} +(-56.5457 - 56.5457i) q^{97} +(7.00000 - 7.00000i) q^{98} +104.517i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 12 q^{5} - 8 q^{6} + 8 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 12 * q^5 - 8 * q^6 + 8 * q^8	$ 4 q - 4 q^{2} + 4 q^{3} + 12 q^{5} - 8 q^{6} + 8 q^{8} + 4 q^{11} + 8 q^{12} + 4 q^{13} + 24 q^{15} - 16 q^{16} - 20 q^{17} - 24 q^{20} - 28 q^{21} - 4 q^{22} - 40 q^{23} - 8 q^{26} - 20 q^{27} - 52 q^{30} + 48 q^{31} + 16 q^{32} - 108 q^{33} - 28 q^{35} + 104 q^{37} + 72 q^{38} + 48 q^{40} + 16 q^{41} + 28 q^{42} + 188 q^{43} - 56 q^{45} + 80 q^{46} - 84 q^{47} - 16 q^{48} + 44 q^{50} + 156 q^{51} + 8 q^{52} + 4 q^{53} - 100 q^{55} + 44 q^{57} - 140 q^{58} + 56 q^{60} - 288 q^{61} - 48 q^{62} - 56 q^{63} + 24 q^{65} + 216 q^{66} - 92 q^{67} + 40 q^{68} + 28 q^{70} - 160 q^{71} - 72 q^{73} + 212 q^{75} - 144 q^{76} + 112 q^{77} - 92 q^{78} - 48 q^{80} + 100 q^{81} - 16 q^{82} + 256 q^{83} + 196 q^{85} - 376 q^{86} - 28 q^{87} + 8 q^{88} - 84 q^{91} - 80 q^{92} - 36 q^{93} - 244 q^{95} + 32 q^{96} - 84 q^{97} + 28 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 12 * q^5 - 8 * q^6 + 8 * q^8 + 4 * q^11 + 8 * q^12 + 4 * q^13 + 24 * q^15 - 16 * q^16 - 20 * q^17 - 24 * q^20 - 28 * q^21 - 4 * q^22 - 40 * q^23 - 8 * q^26 - 20 * q^27 - 52 * q^30 + 48 * q^31 + 16 * q^32 - 108 * q^33 - 28 * q^35 + 104 * q^37 + 72 * q^38 + 48 * q^40 + 16 * q^41 + 28 * q^42 + 188 * q^43 - 56 * q^45 + 80 * q^46 - 84 * q^47 - 16 * q^48 + 44 * q^50 + 156 * q^51 + 8 * q^52 + 4 * q^53 - 100 * q^55 + 44 * q^57 - 140 * q^58 + 56 * q^60 - 288 * q^61 - 48 * q^62 - 56 * q^63 + 24 * q^65 + 216 * q^66 - 92 * q^67 + 40 * q^68 + 28 * q^70 - 160 * q^71 - 72 * q^73 + 212 * q^75 - 144 * q^76 + 112 * q^77 - 92 * q^78 - 48 * q^80 + 100 * q^81 - 16 * q^82 + 256 * q^83 + 196 * q^85 - 376 * q^86 - 28 * q^87 + 8 * q^88 - 84 * q^91 - 80 * q^92 - 36 * q^93 - 244 * q^95 + 32 * q^96 - 84 * q^97 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	2.87083	−	2.87083i	0.956943	−	0.956943i	−0.0421677	−	0.999111i	$-0.513426\pi$
$3$	2.87083	−	2.87083i	0.956943	−	0.956943i	0.999111	+	0.0421677i	$0.0134264\pi$
$4$			2.00000i			0.500000i
$5$	4.87083	+	1.12917i	0.974166	+	0.225834i
$5$	4.87083	+	1.12917i	0.974166	+	0.225834i
$6$	−5.74166			−0.956943
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	7.48331i		−	0.831479i
$10$	−3.74166	−	6.00000i	−0.374166	−	0.600000i
$11$	−13.9666			−1.26969			−0.634847	−	0.772638i	$-0.718937\pi$
$11$	−13.9666			−1.26969			−0.634847	+	0.772638i	$0.718937\pi$
$12$	5.74166	+	5.74166i	0.478471	+	0.478471i
$13$	6.61249	−	6.61249i	0.508653	−	0.508653i	−0.405460	−	0.914113i	$-0.632889\pi$
$13$	6.61249	−	6.61249i	0.508653	−	0.508653i	0.914113	+	0.405460i	$0.132889\pi$
$14$			3.74166i			0.267261i
$15$	17.2250	−	10.7417i	1.14833	−	0.716110i
$16$	−4.00000			−0.250000
$17$	8.09580	+	8.09580i	0.476224	+	0.476224i	0.903922	−	0.427698i	$-0.140675\pi$
$17$	8.09580	+	8.09580i	0.476224	+	0.476224i	−0.427698	+	0.903922i	$0.640675\pi$
$18$	−7.48331	+	7.48331i	−0.415740	+	0.415740i
$19$			14.2583i			0.750439i	0.926936	+	0.375220i	$0.122433\pi$
$19$			14.2583i			0.750439i	−0.926936	+	0.375220i	$0.877567\pi$
$20$	−2.25834	+	9.74166i	−0.112917	+	0.487083i
$21$	−10.7417			−0.511507
$22$	13.9666	+	13.9666i	0.634847	+	0.634847i
$23$	−28.7083	+	28.7083i	−1.24819	+	1.24819i	−0.291666	+	0.956520i	$0.594210\pi$
$23$	−28.7083	+	28.7083i	−1.24819	+	1.24819i	−0.956520	+	0.291666i	$0.905790\pi$
$24$		−	11.4833i		−	0.478471i
$25$	22.4499	+	11.0000i	0.897998	+	0.440000i
$26$	−13.2250			−0.508653
$27$	4.35414	+	4.35414i	0.161265	+	0.161265i
$28$	3.74166	−	3.74166i	0.133631	−	0.133631i
$29$		−	20.0334i		−	0.690806i	−0.938454	−	0.345403i	$-0.887742\pi$
$29$		−	20.0334i		−	0.690806i	0.938454	−	0.345403i	$-0.112258\pi$
$30$	−27.9666	−	6.48331i	−0.932221	−	0.216110i
$31$	0.775028			0.0250009			0.0125004	−	0.999922i	$-0.496021\pi$
$31$	0.775028			0.0250009			0.0125004	+	0.999922i	$0.496021\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−40.0958	+	40.0958i	−1.21502	+	1.21502i
$34$		−	16.1916i		−	0.476224i
$35$	−7.00000	−	11.2250i	−0.200000	−	0.320713i
$36$	14.9666			0.415740
$37$	37.2250	+	37.2250i	1.00608	+	1.00608i	0.999981	+	0.00609893i	$0.00194136\pi$
$37$	37.2250	+	37.2250i	1.00608	+	1.00608i	0.00609893	+	0.999981i	$0.498059\pi$
$38$	14.2583	−	14.2583i	0.375220	−	0.375220i
$39$		−	37.9666i		−	0.973503i
$40$	12.0000	−	7.48331i	0.300000	−	0.187083i
$41$	−29.6749			−0.723778			−0.361889	−	0.932221i	$-0.617868\pi$
$41$	−29.6749			−0.723778			−0.361889	+	0.932221i	$0.617868\pi$
$42$	10.7417	+	10.7417i	0.255754	+	0.255754i
$43$	54.4833	−	54.4833i	1.26705	−	1.26705i	0.319451	−	0.947603i	$-0.396501\pi$
$43$	54.4833	−	54.4833i	1.26705	−	1.26705i	0.947603	−	0.319451i	$-0.103499\pi$
$44$		−	27.9333i		−	0.634847i
$45$	8.44994	−	36.4499i	0.187777	−	0.809999i
$46$	57.4166			1.24819
$47$	−64.0291	−	64.0291i	−1.36232	−	1.36232i	−0.870952	−	0.491369i	$-0.836497\pi$
$47$	−64.0291	−	64.0291i	−1.36232	−	1.36232i	−0.491369	−	0.870952i	$-0.663503\pi$
$48$	−11.4833	+	11.4833i	−0.239236	+	0.239236i
$49$			7.00000i			0.142857i
$50$	−11.4499	−	33.4499i	−0.228999	−	0.668999i
$51$	46.4833			0.911438
$52$	13.2250	+	13.2250i	0.254326	+	0.254326i
$53$	−17.7083	+	17.7083i	−0.334119	+	0.334119i	−0.854148	−	0.520030i	$-0.825921\pi$
$53$	−17.7083	+	17.7083i	−0.334119	+	0.334119i	0.520030	+	0.854148i	$0.325921\pi$
$54$		−	8.70829i		−	0.161265i
$55$	−68.0291	−	15.7707i	−1.23689	−	0.286740i
$56$	−7.48331			−0.133631
$57$	40.9333	+	40.9333i	0.718127	+	0.718127i
$58$	−20.0334	+	20.0334i	−0.345403	+	0.345403i
$59$			60.1249i			1.01907i	0.860451	+	0.509533i	$0.170182\pi$
$59$			60.1249i			1.01907i	−0.860451	+	0.509533i	$0.829818\pi$
$60$	21.4833	+	34.4499i	0.358055	+	0.574166i
$61$	−86.9666			−1.42568			−0.712841	−	0.701325i	$-0.752592\pi$
$61$	−86.9666			−1.42568			−0.712841	+	0.701325i	$0.752592\pi$
$62$	−0.775028	−	0.775028i	−0.0125004	−	0.0125004i
$63$	−14.0000	+	14.0000i	−0.222222	+	0.222222i
$64$		−	8.00000i		−	0.125000i
$65$	39.6749	−	24.7417i	0.610383	−	0.380641i
$66$	80.1916			1.21502
$67$	−41.7083	−	41.7083i	−0.622512	−	0.622512i	0.323661	−	0.946173i	$-0.395086\pi$
$67$	−41.7083	−	41.7083i	−0.622512	−	0.622512i	−0.946173	+	0.323661i	$0.895086\pi$
$68$	−16.1916	+	16.1916i	−0.238112	+	0.238112i
$69$			164.833i			2.38889i
$70$	−4.22497	+	18.2250i	−0.0603567	+	0.260357i
$71$	−47.4833			−0.668779			−0.334390	−	0.942435i	$-0.608530\pi$
$71$	−47.4833			−0.668779			−0.334390	+	0.942435i	$0.608530\pi$
$72$	−14.9666	−	14.9666i	−0.207870	−	0.207870i
$73$	34.3832	−	34.3832i	0.471003	−	0.471003i	−0.431236	−	0.902239i	$-0.641922\pi$
$73$	34.3832	−	34.3832i	0.471003	−	0.471003i	0.902239	+	0.431236i	$0.141922\pi$
$74$		−	74.4499i		−	1.00608i
$75$	96.0291	−	32.8708i	1.28039	−	0.438278i
$76$	−28.5167			−0.375220
$77$	26.1292	+	26.1292i	0.339340	+	0.339340i
$78$	−37.9666	+	37.9666i	−0.486752	+	0.486752i
$79$		−	9.13348i		−	0.115614i	−0.998328	−	0.0578068i	$-0.981589\pi$
$79$		−	9.13348i		−	0.115614i	0.998328	−	0.0578068i	$-0.0184108\pi$
$80$	−19.4833	−	4.51669i	−0.243541	−	0.0564586i
$81$	92.3498			1.14012
$82$	29.6749	+	29.6749i	0.361889	+	0.361889i
$83$	78.9666	−	78.9666i	0.951405	−	0.951405i	−0.0474676	−	0.998873i	$-0.515115\pi$
$83$	78.9666	−	78.9666i	0.951405	−	0.951405i	0.998873	+	0.0474676i	$0.0151151\pi$
$84$		−	21.4833i		−	0.255754i
$85$	30.2917	+	48.5748i	0.356373	+	0.571468i
$86$	−108.967			−1.26705
$87$	−57.5124	−	57.5124i	−0.661062	−	0.661062i
$88$	−27.9333	+	27.9333i	−0.317423	+	0.317423i
$89$			80.0000i			0.898876i	0.893311	+	0.449438i	$0.148376\pi$
$89$			80.0000i			0.898876i	−0.893311	+	0.449438i	$0.851624\pi$
$90$	−44.8999	+	28.0000i	−0.498888	+	0.311111i
$91$	−24.7417			−0.271886
$92$	−57.4166	−	57.4166i	−0.624093	−	0.624093i
$93$	2.22497	−	2.22497i	0.0239244	−	0.0239244i
$94$			128.058i			1.36232i
$95$	−16.1001	+	69.4499i	−0.169475	+	0.731052i
$96$	22.9666			0.239236
$97$	−56.5457	−	56.5457i	−0.582946	−	0.582946i	0.352766	−	0.935712i	$-0.385241\pi$
$97$	−56.5457	−	56.5457i	−0.582946	−	0.582946i	−0.935712	+	0.352766i	$0.885241\pi$
$98$	7.00000	−	7.00000i	0.0714286	−	0.0714286i
$99$			104.517i			1.05572i
$100$	−22.0000	+	44.8999i	−0.220000	+	0.448999i
$101$	−76.5748			−0.758166			−0.379083	−	0.925363i	$-0.623761\pi$
$101$	−76.5748			−0.758166			−0.379083	+	0.925363i	$0.623761\pi$
$102$	−46.4833	−	46.4833i	−0.455719	−	0.455719i
$103$	56.5457	−	56.5457i	0.548988	−	0.548988i	−0.377160	−	0.926148i	$-0.623099\pi$
$103$	56.5457	−	56.5457i	0.548988	−	0.548988i	0.926148	+	0.377160i	$0.123099\pi$
$104$		−	26.4499i		−	0.254326i
$105$	−52.3208	−	12.1292i	−0.498293	−	0.115516i
$106$	35.4166			0.334119
$107$	−27.3832	−	27.3832i	−0.255918	−	0.255918i	0.567474	−	0.823392i	$-0.307921\pi$
$107$	−27.3832	−	27.3832i	−0.255918	−	0.255918i	−0.823392	+	0.567474i	$0.807921\pi$
$108$	−8.70829	+	8.70829i	−0.0806323	+	0.0806323i
$109$		−	154.867i		−	1.42079i	−0.703801	−	0.710397i	$-0.748515\pi$
$109$		−	154.867i		−	1.42079i	0.703801	−	0.710397i	$-0.251485\pi$
$110$	52.2583	+	83.7998i	0.475076	+	0.761816i
$111$	213.733			1.92552
$112$	7.48331	+	7.48331i	0.0668153	+	0.0668153i
$113$	99.0247	−	99.0247i	0.876325	−	0.876325i	−0.116827	−	0.993152i	$-0.537272\pi$
$113$	99.0247	−	99.0247i	0.876325	−	0.876325i	0.993152	+	0.116827i	$0.0372723\pi$
$114$		−	81.8665i		−	0.718127i
$115$	−172.250	+	107.417i	−1.49782	+	0.934057i
$116$	40.0667			0.345403
$117$	−49.4833	−	49.4833i	−0.422934	−	0.422934i
$118$	60.1249	−	60.1249i	0.509533	−	0.509533i
$119$		−	30.2917i		−	0.254552i
$120$	12.9666	−	55.9333i	0.108055	−	0.466110i
$121$	74.0667			0.612122
$122$	86.9666	+	86.9666i	0.712841	+	0.712841i
$123$	−85.1916	+	85.1916i	−0.692615	+	0.692615i
$124$			1.55006i			0.0125004i
$125$	96.9289	+	78.9289i	0.775432	+	0.631432i
$126$	28.0000			0.222222
$127$	64.2917	+	64.2917i	0.506234	+	0.506234i	0.913368	−	0.407134i	$-0.133472\pi$
$127$	64.2917	+	64.2917i	0.506234	+	0.506234i	−0.407134	+	0.913368i	$0.633472\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	312.825i		−	2.42500i
$130$	−64.4166	−	14.9333i	−0.495512	−	0.114871i
$131$	146.633			1.11934			0.559668	−	0.828717i	$-0.310929\pi$
$131$	146.633			1.11934			0.559668	+	0.828717i	$0.310929\pi$
$132$	−80.1916	−	80.1916i	−0.607512	−	0.607512i
$133$	26.6749	−	26.6749i	0.200563	−	0.200563i
$134$			83.4166i			0.622512i
$135$	16.2917	+	26.1249i	0.120679	+	0.193517i
$136$	32.3832			0.238112
$137$	−7.34983	−	7.34983i	−0.0536484	−	0.0536484i	0.679774	−	0.733422i	$-0.262078\pi$
$137$	−7.34983	−	7.34983i	−0.0536484	−	0.0536484i	−0.733422	+	0.679774i	$0.762078\pi$
$138$	164.833	−	164.833i	1.19444	−	1.19444i
$139$			53.8665i			0.387529i	0.981048	+	0.193764i	$0.0620698\pi$
$139$			53.8665i			0.387529i	−0.981048	+	0.193764i	$0.937930\pi$
$140$	22.4499	−	14.0000i	0.160357	−	0.100000i
$141$	−367.633			−2.60733
$142$	47.4833	+	47.4833i	0.334390	+	0.334390i
$143$	−92.3541	+	92.3541i	−0.645833	+	0.645833i
$144$			29.9333i			0.207870i
$145$	22.6211	−	97.5791i	0.156008	−	0.672959i
$146$	−68.7664			−0.471003
$147$	20.0958	+	20.0958i	0.136706	+	0.136706i
$148$	−74.4499	+	74.4499i	−0.503040	+	0.503040i
$149$		−	84.6502i		−	0.568122i	−0.958806	−	0.284061i	$-0.908318\pi$
$149$		−	84.6502i		−	0.568122i	0.958806	−	0.284061i	$-0.0916818\pi$
$150$	−128.900	−	63.1582i	−0.859333	−	0.421055i
$151$	−21.8331			−0.144590			−0.0722952	−	0.997383i	$-0.523032\pi$
$151$	−21.8331			−0.144590			−0.0722952	+	0.997383i	$0.523032\pi$
$152$	28.5167	+	28.5167i	0.187610	+	0.187610i
$153$	60.5834	−	60.5834i	0.395970	−	0.395970i
$154$		−	52.2583i		−	0.339340i
$155$	3.77503	+	0.875139i	0.0243550	+	0.00564606i
$156$	75.9333			0.486752
$157$	34.8331	+	34.8331i	0.221867	+	0.221867i	0.809284	−	0.587417i	$-0.199855\pi$
$157$	34.8331	+	34.8331i	0.221867	+	0.221867i	−0.587417	+	0.809284i	$0.699855\pi$
$158$	−9.13348	+	9.13348i	−0.0578068	+	0.0578068i
$159$			101.675i			0.639465i
$160$	14.9666	+	24.0000i	0.0935414	+	0.150000i
$161$	107.417			0.667184
$162$	−92.3498	−	92.3498i	−0.570061	−	0.570061i
$163$	−45.2250	+	45.2250i	−0.277454	+	0.277454i	−0.832092	−	0.554638i	$-0.812857\pi$
$163$	−45.2250	+	45.2250i	−0.277454	+	0.277454i	0.554638	+	0.832092i	$0.312857\pi$
$164$		−	59.3498i		−	0.361889i
$165$	−240.575	+	150.025i	−1.45803	+	0.909241i
$166$	−157.933			−0.951405
$167$	−78.0377	−	78.0377i	−0.467292	−	0.467292i	0.433744	−	0.901036i	$-0.357192\pi$
$167$	−78.0377	−	78.0377i	−0.467292	−	0.467292i	−0.901036	+	0.433744i	$0.857192\pi$
$168$	−21.4833	+	21.4833i	−0.127877	+	0.127877i
$169$			81.5501i			0.482545i
$170$	18.2831	−	78.8665i	0.107548	−	0.463921i
$171$	106.700			0.623975
$172$	108.967	+	108.967i	0.633527	+	0.633527i
$173$	−102.087	+	102.087i	−0.590099	+	0.590099i	−0.937658	−	0.347559i	$-0.887011\pi$
$173$	−102.087	+	102.087i	−0.590099	+	0.590099i	0.347559	+	0.937658i	$0.387011\pi$
$174$			115.025i			0.661062i
$175$	−21.4209	−	62.5791i	−0.122405	−	0.357595i
$176$	55.8665			0.317423
$177$	172.608	+	172.608i	0.975187	+	0.975187i
$178$	80.0000	−	80.0000i	0.449438	−	0.449438i
$179$			248.250i			1.38687i	0.720519	+	0.693435i	$0.243904\pi$
$179$			248.250i			1.38687i	−0.720519	+	0.693435i	$0.756096\pi$
$180$	72.8999	+	16.8999i	0.404999	+	0.0938883i
$181$	−17.1582			−0.0947969			−0.0473984	−	0.998876i	$-0.515093\pi$
$181$	−17.1582			−0.0947969			−0.0473984	+	0.998876i	$0.515093\pi$
$182$	24.7417	+	24.7417i	0.135943	+	0.135943i
$183$	−249.666	+	249.666i	−1.36430	+	1.36430i
$184$			114.833i			0.624093i
$185$	139.283	+	223.350i	0.752882	+	1.20730i
$186$	−4.44994			−0.0239244
$187$	−113.071	−	113.071i	−0.604658	−	0.604658i
$188$	128.058	−	128.058i	0.681160	−	0.681160i
$189$		−	16.2917i		−	0.0861995i
$190$	85.5501	−	53.3498i	0.450263	−	0.280789i
$191$	200.916			1.05192			0.525958	−	0.850510i	$-0.323707\pi$
$191$	200.916			1.05192			0.525958	+	0.850510i	$0.323707\pi$
$192$	−22.9666	−	22.9666i	−0.119618	−	0.119618i
$193$	121.800	−	121.800i	0.631087	−	0.631087i	−0.317254	−	0.948341i	$-0.602761\pi$
$193$	121.800	−	121.800i	0.631087	−	0.631087i	0.948341	+	0.317254i	$0.102761\pi$
$194$			113.091i			0.582946i
$195$	42.8708	−	184.929i	0.219850	−	0.948354i
$196$	−14.0000			−0.0714286
$197$	−215.125	−	215.125i	−1.09200	−	1.09200i	−0.995315	−	0.0966898i	$-0.969175\pi$
$197$	−215.125	−	215.125i	−1.09200	−	1.09200i	−0.0966898	−	0.995315i	$-0.530825\pi$
$198$	104.517	−	104.517i	0.527862	−	0.527862i
$199$		−	93.2917i		−	0.468803i	−0.972140	−	0.234401i	$-0.924687\pi$
$199$		−	93.2917i		−	0.468803i	0.972140	−	0.234401i	$-0.0753130\pi$
$200$	66.8999	−	22.8999i	0.334499	−	0.114499i
$201$	−239.475			−1.19142
$202$	76.5748	+	76.5748i	0.379083	+	0.379083i
$203$	−37.4790	+	37.4790i	−0.184626	+	0.184626i
$204$			92.9666i			0.455719i
$205$	−144.541	−	33.5081i	−0.705080	−	0.163454i
$206$	−113.091			−0.548988
$207$	214.833	+	214.833i	1.03784	+	1.03784i
$208$	−26.4499	+	26.4499i	−0.127163	+	0.127163i
$209$		−	199.141i		−	0.952828i
$210$	40.1916	+	64.4499i	0.191389	+	0.306904i
$211$	−74.3498			−0.352369			−0.176184	−	0.984357i	$-0.556376\pi$
$211$	−74.3498			−0.352369			−0.176184	+	0.984357i	$0.556376\pi$
$212$	−35.4166	−	35.4166i	−0.167059	−	0.167059i
$213$	−136.316	+	136.316i	−0.639983	+	0.639983i
$214$			54.7664i			0.255918i
$215$	326.900	−	203.858i	1.52046	−	0.948176i
$216$	17.4166			0.0806323
$217$	−1.44994	−	1.44994i	−0.00668177	−	0.00668177i
$218$	−154.867	+	154.867i	−0.710397	+	0.710397i
$219$		−	197.417i		−	0.901446i
$220$	31.5414	−	136.058i	0.143370	−	0.618446i
$221$	107.067			0.484465
$222$	−213.733	−	213.733i	−0.962761	−	0.962761i
$223$	−112.929	+	112.929i	−0.506408	+	0.506408i	−0.913422	−	0.407014i	$-0.866570\pi$
$223$	−112.929	+	112.929i	−0.506408	+	0.506408i	0.407014	+	0.913422i	$0.366570\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	82.3165	−	168.000i	0.365851	−	0.746667i
$226$	−198.049			−0.876325
$227$	85.7793	+	85.7793i	0.377883	+	0.377883i	0.870338	−	0.492455i	$-0.163900\pi$
$227$	85.7793	+	85.7793i	0.377883	+	0.377883i	−0.492455	+	0.870338i	$0.663900\pi$
$228$	−81.8665	+	81.8665i	−0.359064	+	0.359064i
$229$			215.875i			0.942686i	0.881950	+	0.471343i	$0.156231\pi$
$229$			215.875i			0.942686i	−0.881950	+	0.471343i	$0.843769\pi$
$230$	279.666	+	64.8331i	1.21594	+	0.281883i
$231$	150.025			0.649458
$232$	−40.0667	−	40.0667i	−0.172701	−	0.172701i
$233$	−77.5501	+	77.5501i	−0.332833	+	0.332833i	−0.853661	−	0.520828i	$-0.825623\pi$
$233$	−77.5501	+	77.5501i	−0.332833	+	0.332833i	0.520828	+	0.853661i	$0.325623\pi$
$234$			98.9666i			0.422934i
$235$	−239.575	−	384.174i	−1.01947	−	1.63478i
$236$	−120.250			−0.509533
$237$	−26.2207	−	26.2207i	−0.110636	−	0.110636i
$238$	−30.2917	+	30.2917i	−0.127276	+	0.127276i
$239$		−	30.4661i		−	0.127473i	−0.997967	−	0.0637366i	$-0.979698\pi$
$239$		−	30.4661i		−	0.127473i	0.997967	−	0.0637366i	$-0.0203017\pi$
$240$	−68.8999	+	42.9666i	−0.287083	+	0.179028i
$241$	40.3337			0.167360			0.0836799	−	0.996493i	$-0.473333\pi$
$241$	40.3337			0.167360			0.0836799	+	0.996493i	$0.473333\pi$
$242$	−74.0667	−	74.0667i	−0.306061	−	0.306061i
$243$	225.933	−	225.933i	0.929766	−	0.929766i
$244$		−	173.933i		−	0.712841i
$245$	−7.90420	+	34.0958i	−0.0322620	+	0.139167i
$246$	170.383			0.692615
$247$	94.2831	+	94.2831i	0.381713	+	0.381713i
$248$	1.55006	−	1.55006i	0.00625022	−	0.00625022i
$249$		−	453.399i		−	1.82088i
$250$	−18.0000	−	175.858i	−0.0720000	−	0.703432i
$251$	−95.1669			−0.379151			−0.189575	−	0.981866i	$-0.560711\pi$
$251$	−95.1669			−0.379151			−0.189575	+	0.981866i	$0.560711\pi$
$252$	−28.0000	−	28.0000i	−0.111111	−	0.111111i
$253$	400.958	−	400.958i	1.58481	−	1.58481i
$254$		−	128.583i		−	0.506234i
$255$	226.412	+	52.4876i	0.887891	+	0.205834i
$256$	16.0000			0.0625000
$257$	270.566	+	270.566i	1.05279	+	1.05279i	0.998527	+	0.0542599i	$0.0172799\pi$
$257$	270.566	+	270.566i	1.05279	+	1.05279i	0.0542599	+	0.998527i	$0.482720\pi$
$258$	−312.825	+	312.825i	−1.21250	+	1.21250i
$259$		−	139.283i		−	0.537773i
$260$	49.4833	+	79.3498i	0.190320	+	0.305192i
$261$	−149.916			−0.574391
$262$	−146.633	−	146.633i	−0.559668	−	0.559668i
$263$	183.967	−	183.967i	0.699493	−	0.699493i	−0.264808	−	0.964301i	$-0.585309\pi$
$263$	183.967	−	183.967i	0.699493	−	0.699493i	0.964301	+	0.264808i	$0.0853087\pi$
$264$			160.383i			0.607512i
$265$	−106.250	+	66.2583i	−0.400942	+	0.250031i
$266$	−53.3498			−0.200563
$267$	229.666	+	229.666i	0.860173	+	0.860173i
$268$	83.4166	−	83.4166i	0.311256	−	0.311256i
$269$			22.4994i			0.0836411i	0.999125	+	0.0418205i	$0.0133158\pi$
$269$			22.4994i			0.0836411i	−0.999125	+	0.0418205i	$0.986684\pi$
$270$	9.83315	−	42.4166i	0.0364191	−	0.157098i
$271$	−154.067			−0.568512			−0.284256	−	0.958748i	$-0.591747\pi$
$271$	−154.067			−0.568512			−0.284256	+	0.958748i	$0.591747\pi$
$272$	−32.3832	−	32.3832i	−0.119056	−	0.119056i
$273$	−71.0291	+	71.0291i	−0.260180	+	0.260180i
$274$			14.6997i			0.0536484i
$275$	−313.550	−	153.633i	−1.14018	−	0.558665i
$276$	−329.666			−1.19444
$277$	336.041	+	336.041i	1.21314	+	1.21314i	0.969987	+	0.243157i	$0.0781830\pi$
$277$	336.041	+	336.041i	1.21314	+	1.21314i	0.243157	+	0.969987i	$0.421817\pi$
$278$	53.8665	−	53.8665i	0.193764	−	0.193764i
$279$		−	5.79978i		−	0.0207877i
$280$	−36.4499	−	8.44994i	−0.130178	−	0.0301784i
$281$	283.299			1.00818			0.504091	−	0.863650i	$-0.331828\pi$
$281$	283.299			1.00818			0.504091	+	0.863650i	$0.331828\pi$
$282$	367.633	+	367.633i	1.30366	+	1.30366i
$283$	−193.321	+	193.321i	−0.683112	+	0.683112i	−0.960700	−	0.277588i	$-0.910465\pi$
$283$	−193.321	+	193.321i	−0.683112	+	0.683112i	0.277588	+	0.960700i	$0.410465\pi$
$284$		−	94.9666i		−	0.334390i
$285$	153.158	+	245.600i	0.537397	+	0.861753i
$286$	184.708			0.645833
$287$	55.5167	+	55.5167i	0.193438	+	0.193438i
$288$	29.9333	−	29.9333i	0.103935	−	0.103935i
$289$		−	157.916i		−	0.546422i
$290$	−120.200	+	74.9580i	−0.414484	+	0.258476i
$291$	−324.666			−1.11569
$292$	68.7664	+	68.7664i	0.235501	+	0.235501i
$293$	−346.412	+	346.412i	−1.18229	+	1.18229i	−0.203146	+	0.979148i	$0.565117\pi$
$293$	−346.412	+	346.412i	−1.18229	+	1.18229i	−0.979148	+	0.203146i	$0.934883\pi$
$294$		−	40.1916i		−	0.136706i
$295$	−67.8913	+	292.858i	−0.230140	+	0.992739i
$296$	148.900			0.503040
$297$	−60.8127	−	60.8127i	−0.204757	−	0.204757i
$298$	−84.6502	+	84.6502i	−0.284061	+	0.284061i
$299$			379.666i			1.26979i
$300$	65.7417	+	192.058i	0.219139	+	0.640194i
$301$	−203.858			−0.677269
$302$	21.8331	+	21.8331i	0.0722952	+	0.0722952i
$303$	−219.833	+	219.833i	−0.725522	+	0.725522i
$304$		−	57.0334i		−	0.187610i
$305$	−423.600	−	98.2002i	−1.38885	−	0.321968i
$306$	−121.167			−0.395970
$307$	245.512	+	245.512i	0.799715	+	0.799715i	0.983050	−	0.183336i	$-0.0586896\pi$
$307$	245.512	+	245.512i	0.799715	+	0.799715i	−0.183336	+	0.983050i	$0.558690\pi$
$308$	−52.2583	+	52.2583i	−0.169670	+	0.169670i
$309$		−	324.666i		−	1.05070i
$310$	−2.89989	−	4.65017i	−0.00935448	−	0.0150005i
$311$	325.091			1.04531			0.522655	−	0.852544i	$-0.324942\pi$
$311$	325.091			1.04531			0.522655	+	0.852544i	$0.324942\pi$
$312$	−75.9333	−	75.9333i	−0.243376	−	0.243376i
$313$	228.012	−	228.012i	0.728472	−	0.728472i	−0.241843	−	0.970315i	$-0.577752\pi$
$313$	228.012	−	228.012i	0.728472	−	0.728472i	0.970315	+	0.241843i	$0.0777519\pi$
$314$		−	69.6663i		−	0.221867i
$315$	−84.0000	+	52.3832i	−0.266667	+	0.166296i
$316$	18.2670			0.0578068
$317$	−314.800	−	314.800i	−0.993059	−	0.993059i	0.00691684	−	0.999976i	$-0.497798\pi$
$317$	−314.800	−	314.800i	−0.993059	−	0.993059i	−0.999976	+	0.00691684i	$0.997798\pi$
$318$	101.675	−	101.675i	0.319732	−	0.319732i
$319$			279.799i			0.877112i
$320$	9.03337	−	38.9666i	0.0282293	−	0.121771i
$321$	−157.225			−0.489797
$322$	−107.417	−	107.417i	−0.333592	−	0.333592i
$323$	−115.433	+	115.433i	−0.357377	+	0.357377i
$324$			184.700i			0.570061i
$325$	221.187	−	75.7126i	0.680576	−	0.232962i
$326$	90.4499			0.277454
$327$	−444.595	−	444.595i	−1.35962	−	1.35962i
$328$	−59.3498	+	59.3498i	−0.180945	+	0.180945i
$329$			239.575i			0.728191i
$330$	390.600	+	90.5501i	1.18364	+	0.274394i
$331$	−65.2831			−0.197230			−0.0986149	−	0.995126i	$-0.531441\pi$
$331$	−65.2831			−0.197230			−0.0986149	+	0.995126i	$0.531441\pi$
$332$	157.933	+	157.933i	0.475703	+	0.475703i
$333$	278.566	−	278.566i	0.836535	−	0.836535i
$334$			156.075i			0.467292i
$335$	−156.058	−	250.250i	−0.465845	−	0.747014i
$336$	42.9666			0.127877
$337$	−18.0086	−	18.0086i	−0.0534380	−	0.0534380i	0.679883	−	0.733321i	$-0.262031\pi$
$337$	−18.0086	−	18.0086i	−0.0534380	−	0.0534380i	−0.733321	+	0.679883i	$0.762031\pi$
$338$	81.5501	−	81.5501i	0.241272	−	0.241272i
$339$		−	568.566i		−	1.67719i
$340$	−97.1496	+	60.5834i	−0.285734	+	0.178187i
$341$	−10.8245			−0.0317435
$342$	−106.700	−	106.700i	−0.311987	−	0.311987i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$		−	217.933i		−	0.633527i
$345$	−186.125	+	802.874i	−0.539492	+	2.32717i
$346$	204.174			0.590099
$347$	137.625	+	137.625i	0.396615	+	0.396615i	0.877037	−	0.480422i	$-0.159517\pi$
$347$	137.625	+	137.625i	0.396615	+	0.396615i	−0.480422	+	0.877037i	$0.659517\pi$
$348$	115.025	−	115.025i	0.330531	−	0.330531i
$349$			496.174i			1.42170i	0.703342	+	0.710852i	$0.251690\pi$
$349$			496.174i			1.42170i	−0.703342	+	0.710852i	$0.748310\pi$
$350$	−41.1582	+	84.0000i	−0.117595	+	0.240000i
$351$	57.5834			0.164055
$352$	−55.8665	−	55.8665i	−0.158712	−	0.158712i
$353$	92.1625	−	92.1625i	0.261084	−	0.261084i	−0.564411	−	0.825494i	$-0.690896\pi$
$353$	92.1625	−	92.1625i	0.261084	−	0.261084i	0.825494	+	0.564411i	$0.190896\pi$
$354$		−	345.216i		−	0.975187i
$355$	−231.283	−	53.6168i	−0.651502	−	0.151033i
$356$	−160.000			−0.449438
$357$	−86.9623	−	86.9623i	−0.243592	−	0.243592i
$358$	248.250	−	248.250i	0.693435	−	0.693435i
$359$		−	592.232i		−	1.64967i	−0.565372	−	0.824836i	$-0.691267\pi$
$359$		−	592.232i		−	1.64967i	0.565372	−	0.824836i	$-0.308733\pi$
$360$	−56.0000	−	89.7998i	−0.155556	−	0.249444i
$361$	157.700			0.436841
$362$	17.1582	+	17.1582i	0.0473984	+	0.0473984i
$363$	212.633	−	212.633i	0.585766	−	0.585766i
$364$		−	49.4833i		−	0.135943i
$365$	206.299	−	128.650i	0.565203	−	0.352466i
$366$	499.333			1.36430
$367$	42.0872	+	42.0872i	0.114679	+	0.114679i	0.762118	−	0.647439i	$-0.224160\pi$
$367$	42.0872	+	42.0872i	0.114679	+	0.114679i	−0.647439	+	0.762118i	$0.724160\pi$
$368$	114.833	−	114.833i	0.312047	−	0.312047i
$369$			222.067i			0.601807i
$370$	84.0667	−	362.633i	0.227207	−	0.980089i
$371$	66.2583			0.178594
$372$	4.44994	+	4.44994i	0.0119622	+	0.0119622i
$373$	−160.133	+	160.133i	−0.429312	+	0.429312i	−0.888394	−	0.459082i	$-0.848178\pi$
$373$	−160.133	+	160.133i	−0.429312	+	0.429312i	0.459082	+	0.888394i	$0.348178\pi$
$374$			226.142i			0.604658i
$375$	504.858	−	51.6749i	1.34629	−	0.137800i
$376$	−256.116			−0.681160
$377$	−132.470	−	132.470i	−0.351380	−	0.351380i
$378$	−16.2917	+	16.2917i	−0.0430998	+	0.0430998i
$379$			749.066i			1.97643i	0.153084	+	0.988213i	$0.451080\pi$
$379$			749.066i			1.97643i	−0.153084	+	0.988213i	$0.548920\pi$
$380$	−138.900	−	32.2002i	−0.365526	−	0.0847374i
$381$	369.141			0.968874
$382$	−200.916	−	200.916i	−0.525958	−	0.525958i
$383$	−295.399	+	295.399i	−0.771278	+	0.771278i	−0.978330	−	0.207052i	$-0.933613\pi$
$383$	−295.399	+	295.399i	−0.771278	+	0.771278i	0.207052	+	0.978330i	$0.433613\pi$
$384$			45.9333i			0.119618i
$385$	97.7664	+	156.775i	0.253939	+	0.407208i
$386$	−243.600			−0.631087
$387$	−407.716	−	407.716i	−1.05353	−	1.05353i
$388$	113.091	−	113.091i	0.291473	−	0.291473i
$389$			387.116i			0.995157i	0.867419	+	0.497579i	$0.165777\pi$
$389$			387.116i			0.995157i	−0.867419	+	0.497579i	$0.834223\pi$
$390$	−227.800	+	142.058i	−0.584102	+	0.364252i
$391$	−464.833			−1.18883
$392$	14.0000	+	14.0000i	0.0357143	+	0.0357143i
$393$	420.958	−	420.958i	1.07114	−	1.07114i
$394$			430.250i			1.09200i
$395$	10.3133	−	44.4876i	0.0261095	−	0.112627i
$396$	−209.033			−0.527862
$397$	−282.203	−	282.203i	−0.710840	−	0.710840i	0.255871	−	0.966711i	$-0.417638\pi$
$397$	−282.203	−	282.203i	−0.710840	−	0.710840i	−0.966711	+	0.255871i	$0.917638\pi$
$398$	−93.2917	+	93.2917i	−0.234401	+	0.234401i
$399$		−	153.158i		−	0.383855i
$400$	−89.7998	−	44.0000i	−0.224499	−	0.110000i
$401$	−95.6502			−0.238529			−0.119265	−	0.992863i	$-0.538054\pi$
$401$	−95.6502			−0.238529			−0.119265	+	0.992863i	$0.538054\pi$
$402$	239.475	+	239.475i	0.595708	+	0.595708i
$403$	5.12486	−	5.12486i	0.0127168	−	0.0127168i
$404$		−	153.150i		−	0.379083i
$405$	449.820	+	104.279i	1.11067	+	0.257478i
$406$	74.9580			0.184626
$407$	−519.907	−	519.907i	−1.27741	−	1.27741i
$408$	92.9666	−	92.9666i	0.227859	−	0.227859i
$409$		−	113.875i		−	0.278423i	−0.990263	−	0.139212i	$-0.955543\pi$
$409$		−	113.875i		−	0.278423i	0.990263	−	0.139212i	$-0.0444568\pi$
$410$	111.033	+	178.049i	0.270813	+	0.434267i
$411$	−42.2002			−0.102677
$412$	113.091	+	113.091i	0.274494	+	0.274494i
$413$	112.483	−	112.483i	0.272357	−	0.272357i
$414$		−	429.666i		−	1.03784i
$415$	473.800	−	295.466i	1.14169	−	0.711966i
$416$	52.8999			0.127163
$417$	154.642	+	154.642i	0.370843	+	0.370843i
$418$	−199.141	+	199.141i	−0.476414	+	0.476414i
$419$		−	445.158i		−	1.06243i	−0.847237	−	0.531215i	$-0.821736\pi$
$419$		−	445.158i		−	1.06243i	0.847237	−	0.531215i	$-0.178264\pi$
$420$	24.2583	−	104.642i	0.0577580	−	0.249147i
$421$	164.333			0.390339			0.195169	−	0.980770i	$-0.437474\pi$
$421$	164.333			0.390339			0.195169	+	0.980770i	$0.437474\pi$
$422$	74.3498	+	74.3498i	0.176184	+	0.176184i
$423$	−479.150	+	479.150i	−1.13274	+	1.13274i
$424$			70.8331i			0.167059i
$425$	92.6965	+	270.804i	0.218109	+	0.637186i
$426$	272.633			0.639983
$427$	162.700	+	162.700i	0.381030	+	0.381030i
$428$	54.7664	−	54.7664i	0.127959	−	0.127959i
$429$			530.266i			1.23605i
$430$	−530.758	−	123.042i	−1.23432	−	0.286144i
$431$	466.199			1.08167			0.540834	−	0.841129i	$-0.318109\pi$
$431$	466.199			1.08167			0.540834	+	0.841129i	$0.318109\pi$
$432$	−17.4166	−	17.4166i	−0.0403161	−	0.0403161i
$433$	221.274	−	221.274i	0.511026	−	0.511026i	−0.403814	−	0.914841i	$-0.632316\pi$
$433$	221.274	−	221.274i	0.511026	−	0.511026i	0.914841	+	0.403814i	$0.132316\pi$
$434$			2.89989i			0.00668177i
$435$	−215.192	−	345.074i	−0.494693	−	0.793274i
$436$	309.733			0.710397
$437$	−409.333	−	409.333i	−0.936688	−	0.936688i
$438$	−197.417	+	197.417i	−0.450723	+	0.450723i
$439$			32.5662i			0.0741827i	0.999312	+	0.0370913i	$0.0118092\pi$
$439$			32.5662i			0.0741827i	−0.999312	+	0.0370913i	$0.988191\pi$
$440$	−167.600	+	104.517i	−0.380908	+	0.237538i
$441$	52.3832			0.118783
$442$	−107.067	−	107.067i	−0.242232	−	0.242232i
$443$	312.849	−	312.849i	0.706206	−	0.706206i	−0.259529	−	0.965735i	$-0.583567\pi$
$443$	312.849	−	312.849i	0.706206	−	0.706206i	0.965735	+	0.259529i	$0.0835674\pi$
$444$			427.466i			0.962761i
$445$	−90.3337	+	389.666i	−0.202997	+	0.875655i
$446$	225.858			0.506408
$447$	−243.016	−	243.016i	−0.543660	−	0.543660i
$448$	−14.9666	+	14.9666i	−0.0334077	+	0.0334077i
$449$			276.582i			0.615996i	0.951387	+	0.307998i	$0.0996591\pi$
$449$			276.582i			0.615996i	−0.951387	+	0.307998i	$0.900341\pi$
$450$	−250.316	+	85.6835i	−0.556259	+	0.190408i
$451$	414.459			0.918977
$452$	198.049	+	198.049i	0.438163	+	0.438163i
$453$	−62.6792	+	62.6792i	−0.138365	+	0.138365i
$454$		−	171.559i		−	0.377883i
$455$	−120.512	−	27.9376i	−0.264862	−	0.0614013i
$456$	163.733			0.359064
$457$	77.4413	+	77.4413i	0.169456	+	0.169456i	0.786740	−	0.617284i	$-0.211767\pi$
$457$	77.4413	+	77.4413i	0.169456	+	0.169456i	−0.617284	+	0.786740i	$0.711767\pi$
$458$	215.875	−	215.875i	0.471343	−	0.471343i
$459$			70.5006i			0.153596i
$460$	−214.833	−	344.499i	−0.467029	−	0.748912i
$461$	−615.600			−1.33536			−0.667678	−	0.744450i	$-0.732712\pi$
$461$	−615.600			−1.33536			−0.667678	+	0.744450i	$0.732712\pi$
$462$	−150.025	−	150.025i	−0.324729	−	0.324729i
$463$	146.566	−	146.566i	0.316558	−	0.316558i	−0.530886	−	0.847443i	$-0.678141\pi$
$463$	146.566	−	146.566i	0.316558	−	0.316558i	0.847443	+	0.530886i	$0.178141\pi$
$464$			80.1335i			0.172701i
$465$	13.3498	−	8.32508i	0.0287093	−	0.0179034i
$466$	155.100			0.332833
$467$	−95.0711	−	95.0711i	−0.203578	−	0.203578i	0.597953	−	0.801531i	$-0.295981\pi$
$467$	−95.0711	−	95.0711i	−0.203578	−	0.203578i	−0.801531	+	0.597953i	$0.795981\pi$
$468$	98.9666	−	98.9666i	0.211467	−	0.211467i
$469$			156.058i			0.332747i
$470$	−144.600	+	623.749i	−0.307659	+	1.32713i
$471$	200.000			0.424628
$472$	120.250	+	120.250i	0.254766	+	0.254766i
$473$	−760.948	+	760.948i	−1.60877	+	1.60877i
$474$			52.4413i			0.110636i
$475$	−156.842	+	320.099i	−0.330193	+	0.673893i
$476$	60.5834			0.127276
$477$	132.517	+	132.517i	0.277813	+	0.277813i
$478$	−30.4661	+	30.4661i	−0.0637366	+	0.0637366i
$479$			32.0667i			0.0669452i	0.999440	+	0.0334726i	$0.0106566\pi$
$479$			32.0667i			0.0669452i	−0.999440	+	0.0334726i	$0.989343\pi$
$480$	111.867	+	25.9333i	0.233055	+	0.0540276i
$481$	492.299			1.02349
$482$	−40.3337	−	40.3337i	−0.0836799	−	0.0836799i
$483$	308.375	−	308.375i	0.638457	−	0.638457i
$484$			148.133i			0.306061i
$485$	−211.575	−	339.274i	−0.436237	−	0.699535i
$486$	−451.867			−0.929766
$487$	−449.324	−	449.324i	−0.922636	−	0.922636i	0.0745786	−	0.997215i	$-0.476239\pi$
$487$	−449.324	−	449.324i	−0.922636	−	0.922636i	−0.997215	+	0.0745786i	$0.976239\pi$
$488$	−173.933	+	173.933i	−0.356421	+	0.356421i
$489$			259.666i			0.531015i
$490$	42.0000	−	26.1916i	0.0857143	−	0.0534522i
$491$	322.216			0.656245			0.328123	−	0.944635i	$-0.393584\pi$
$491$	322.216			0.656245			0.328123	+	0.944635i	$0.393584\pi$
$492$	−170.383	−	170.383i	−0.346307	−	0.346307i
$493$	162.186	−	162.186i	0.328978	−	0.328978i
$494$		−	188.566i		−	0.381713i
$495$	−118.017	+	509.083i	−0.238419	+	1.02845i
$496$	−3.10011			−0.00625022
$497$	88.8331	+	88.8331i	0.178739	+	0.178739i
$498$	−453.399	+	453.399i	−0.910440	+	0.910440i
$499$			925.648i			1.85501i	0.373816	+	0.927503i	$0.378049\pi$
$499$			925.648i			1.85501i	−0.373816	+	0.927503i	$0.621951\pi$
$500$	−157.858	+	193.858i	−0.315716	+	0.387716i
$501$	−448.066			−0.894343
$502$	95.1669	+	95.1669i	0.189575	+	0.189575i
$503$	158.029	−	158.029i	0.314173	−	0.314173i	−0.532351	−	0.846524i	$-0.678691\pi$
$503$	158.029	−	158.029i	0.314173	−	0.314173i	0.846524	+	0.532351i	$0.178691\pi$
$504$			56.0000i			0.111111i
$505$	−372.983	−	86.4661i	−0.738580	−	0.171220i
$506$	−801.916			−1.58481
$507$	234.116	+	234.116i	0.461768	+	0.461768i
$508$	−128.583	+	128.583i	−0.253117	+	0.253117i
$509$		−	972.299i		−	1.91021i	−0.296260	−	0.955107i	$-0.595740\pi$
$509$		−	972.299i		−	1.91021i	0.296260	−	0.955107i	$-0.404260\pi$
$510$	−173.925	−	278.900i	−0.341029	−	0.546863i
$511$	−128.650			−0.251762
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−62.0829	+	62.0829i	−0.121019	+	0.121019i
$514$		−	541.132i		−	1.05279i
$515$	339.274	−	211.575i	0.658785	−	0.410825i
$516$	625.649			1.21250
$517$	894.270	+	894.270i	1.72973	+	1.72973i
$518$	−139.283	+	139.283i	−0.268886	+	0.268886i
$519$			586.150i			1.12938i
$520$	29.8665	−	128.833i	0.0574356	−	0.247756i
$521$	−178.525			−0.342659			−0.171329	−	0.985214i	$-0.554806\pi$
$521$	−178.525			−0.342659			−0.171329	+	0.985214i	$0.554806\pi$
$522$	149.916	+	149.916i	0.287195	+	0.287195i
$523$	412.241	−	412.241i	0.788224	−	0.788224i	−0.192979	−	0.981203i	$-0.561815\pi$
$523$	412.241	−	412.241i	0.788224	−	0.788224i	0.981203	+	0.192979i	$0.0618149\pi$
$524$			293.266i			0.559668i
$525$	−241.150	−	118.158i	−0.459333	−	0.225063i
$526$	−367.933			−0.699493
$527$	6.27447	+	6.27447i	0.0119060	+	0.0119060i
$528$	160.383	−	160.383i	0.303756	−	0.303756i
$529$		−	1119.33i		−	2.11594i
$530$	172.508	+	39.9914i	0.325487	+	0.0754554i
$531$	449.933			0.847332
$532$	53.3498	+	53.3498i	0.100282	+	0.100282i
$533$	−196.225	+	196.225i	−0.368152	+	0.368152i
$534$		−	459.333i		−	0.860173i
$535$	−102.459	−	164.299i	−0.191511	−	0.307101i
$536$	−166.833			−0.311256
$537$	712.682	+	712.682i	1.32716	+	1.32716i
$538$	22.4994	−	22.4994i	0.0418205	−	0.0418205i
$539$		−	97.7664i		−	0.181385i
$540$	−52.2497	+	32.5834i	−0.0967587	+	0.0603397i
$541$	485.133			0.896735			0.448367	−	0.893849i	$-0.352006\pi$
$541$	485.133			0.896735			0.448367	+	0.893849i	$0.352006\pi$
$542$	154.067	+	154.067i	0.284256	+	0.284256i
$543$	−49.2583	+	49.2583i	−0.0907152	+	0.0907152i
$544$			64.7664i			0.119056i
$545$	174.871	−	754.328i	0.320864	−	1.38409i
$546$	142.058			0.260180
$547$	92.0172	+	92.0172i	0.168222	+	0.168222i	0.786197	−	0.617976i	$-0.212047\pi$
$547$	92.0172	+	92.0172i	0.168222	+	0.168222i	−0.617976	+	0.786197i	$0.712047\pi$
$548$	14.6997	−	14.6997i	0.0268242	−	0.0268242i
$549$			650.799i			1.18543i
$550$	159.917	+	467.183i	0.290758	+	0.849424i
$551$	285.643			0.518408
$552$	329.666	+	329.666i	0.597222	+	0.597222i
$553$	−17.0872	+	17.0872i	−0.0308991	+	0.0308991i
$554$		−	672.082i		−	1.21314i
$555$	1041.06	+	241.341i	1.87578	+	0.434849i
$556$	−107.733			−0.193764
$557$	−201.283	−	201.283i	−0.361370	−	0.361370i	0.502947	−	0.864317i	$-0.332249\pi$
$557$	−201.283	−	201.283i	−0.361370	−	0.361370i	−0.864317	+	0.502947i	$0.832249\pi$
$558$	−5.79978	+	5.79978i	−0.0103939	+	0.0103939i
$559$		−	720.540i		−	1.28898i
$560$	28.0000	+	44.8999i	0.0500000	+	0.0801784i
$561$	−649.215			−1.15725
$562$	−283.299	−	283.299i	−0.504091	−	0.504091i
$563$	−200.949	+	200.949i	−0.356926	+	0.356926i	−0.862679	−	0.505753i	$-0.831215\pi$
$563$	−200.949	+	200.949i	−0.356926	+	0.356926i	0.505753	+	0.862679i	$0.331215\pi$
$564$		−	735.266i		−	1.30366i
$565$	594.148	−	370.517i	1.05159	−	0.655782i
$566$	386.642			0.683112
$567$	−172.771	−	172.771i	−0.304710	−	0.304710i
$568$	−94.9666	+	94.9666i	−0.167195	+	0.167195i
$569$		−	724.349i		−	1.27302i	−0.771268	−	0.636510i	$-0.780377\pi$
$569$		−	724.349i		−	1.27302i	0.771268	−	0.636510i	$-0.219623\pi$
$570$	92.4413	−	398.758i	0.162178	−	0.699575i
$571$	−650.850			−1.13984			−0.569922	−	0.821699i	$-0.693026\pi$
$571$	−650.850			−1.13984			−0.569922	+	0.821699i	$0.693026\pi$
$572$	−184.708	−	184.708i	−0.322917	−	0.322917i
$573$	576.795	−	576.795i	1.00662	−	1.00662i
$574$		−	111.033i		−	0.193438i
$575$	−960.291	+	328.708i	−1.67007	+	0.571667i
$576$	−59.8665			−0.103935
$577$	−758.711	−	758.711i	−1.31492	−	1.31492i	−0.917738	−	0.397187i	$-0.869987\pi$
$577$	−758.711	−	758.711i	−1.31492	−	1.31492i	−0.397187	−	0.917738i	$-0.630013\pi$
$578$	−157.916	+	157.916i	−0.273211	+	0.273211i
$579$		−	699.333i		−	1.20783i
$580$	195.158	+	45.2422i	0.336480	+	0.0780038i
$581$	−295.466			−0.508547
$582$	324.666	+	324.666i	0.557846	+	0.557846i
$583$	247.325	−	247.325i	0.424228	−	0.424228i
$584$		−	137.533i		−	0.235501i
$585$	−185.150	−	296.900i	−0.316495	−	0.507521i
$586$	692.825			1.18229
$587$	422.865	+	422.865i	0.720384	+	0.720384i	0.968683	−	0.248299i	$-0.0798717\pi$
$587$	422.865	+	422.865i	0.720384	+	0.720384i	−0.248299	+	0.968683i	$0.579872\pi$
$588$	−40.1916	+	40.1916i	−0.0683531	+	0.0683531i
$589$			11.0506i			0.0187617i
$590$	360.749	−	224.967i	0.611439	−	0.381299i
$591$	−1235.17			−2.08997
$592$	−148.900	−	148.900i	−0.251520	−	0.251520i
$593$	−633.245	+	633.245i	−1.06787	+	1.06787i	−0.0703447	+	0.997523i	$0.522410\pi$
$593$	−633.245	+	633.245i	−1.06787	+	1.06787i	−0.997523	+	0.0703447i	$0.977590\pi$
$594$			121.625i			0.204757i
$595$	34.2045	−	147.546i	0.0574866	−	0.247976i
$596$	169.300			0.284061
$597$	−267.825	−	267.825i	−0.448617	−	0.448617i
$598$	379.666	−	379.666i	0.634893	−	0.634893i
$599$			688.733i			1.14980i	0.818222	+	0.574902i	$0.194960\pi$
$599$			688.733i			1.14980i	−0.818222	+	0.574902i	$0.805040\pi$
$600$	126.316	−	257.800i	0.210527	−	0.429666i
$601$	−651.739			−1.08443			−0.542213	−	0.840241i	$-0.682413\pi$
$601$	−651.739			−1.08443			−0.542213	+	0.840241i	$0.682413\pi$
$602$	203.858	+	203.858i	0.338634	+	0.338634i
$603$	−312.116	+	312.116i	−0.517606	+	0.517606i
$604$		−	43.6663i		−	0.0722952i
$605$	360.766	+	83.6340i	0.596308	+	0.138238i
$606$	439.666			0.725522
$607$	203.678	+	203.678i	0.335549	+	0.335549i	0.854689	−	0.519140i	$-0.173748\pi$
$607$	203.678	+	203.678i	0.335549	+	0.335549i	−0.519140	+	0.854689i	$0.673748\pi$
$608$	−57.0334	+	57.0334i	−0.0938049	+	0.0938049i
$609$			215.192i			0.353352i
$610$	325.399	+	521.800i	0.533442	+	0.855409i
$611$	−846.783			−1.38590
$612$	121.167	+	121.167i	0.197985	+	0.197985i
$613$	357.766	−	357.766i	0.583632	−	0.583632i	−0.352267	−	0.935899i	$-0.614589\pi$
$613$	357.766	−	357.766i	0.583632	−	0.583632i	0.935899	+	0.352267i	$0.114589\pi$
$614$		−	491.025i		−	0.799715i
$615$	−511.150	+	318.758i	−0.831138	+	0.518305i
$616$	104.517			0.169670
$617$	328.174	+	328.174i	0.531887	+	0.531887i	0.921134	−	0.389246i	$-0.127265\pi$
$617$	328.174	+	328.174i	0.531887	+	0.531887i	−0.389246	+	0.921134i	$0.627265\pi$
$618$	−324.666	+	324.666i	−0.525350	+	0.525350i
$619$			949.733i			1.53430i	0.641466	+	0.767151i	$0.278326\pi$
$619$			949.733i			1.53430i	−0.641466	+	0.767151i	$0.721674\pi$
$620$	−1.75028	+	7.55006i	−0.00282303	+	0.0121775i
$621$	−250.000			−0.402576
$622$	−325.091	−	325.091i	−0.522655	−	0.522655i
$623$	149.666	−	149.666i	0.240235	−	0.240235i
$624$			151.867i			0.243376i
$625$	383.000	+	493.899i	0.612800	+	0.790238i
$626$	−456.024			−0.728472
$627$	−571.700	−	571.700i	−0.911802	−	0.911802i
$628$	−69.6663	+	69.6663i	−0.110934	+	0.110934i
$629$			602.732i			0.958238i
$630$	136.383	+	31.6168i	0.216481	+	0.0501854i
$631$	−646.266			−1.02419			−0.512097	−	0.858928i	$-0.671131\pi$
$631$	−646.266			−1.02419			−0.512097	+	0.858928i	$0.671131\pi$
$632$	−18.2670	−	18.2670i	−0.0289034	−	0.0289034i
$633$	−213.446	+	213.446i	−0.337197	+	0.337197i
$634$			629.600i			0.993059i
$635$	240.558	+	385.750i	0.378831	+	0.607481i
$636$	−203.350			−0.319732
$637$	46.2874	+	46.2874i	0.0726647	+	0.0726647i
$638$	279.799	−	279.799i	0.438556	−	0.438556i
$639$			355.333i			0.556076i
$640$	−48.0000	+	29.9333i	−0.0750000	+	0.0467707i
$641$	409.899			0.639468			0.319734	−	0.947507i	$-0.396407\pi$
$641$	409.899			0.639468			0.319734	+	0.947507i	$0.396407\pi$
$642$	157.225	+	157.225i	0.244899	+	0.244899i
$643$	−125.487	+	125.487i	−0.195158	+	0.195158i	−0.797921	−	0.602763i	$-0.794067\pi$
$643$	−125.487	+	125.487i	−0.195158	+	0.195158i	0.602763	+	0.797921i	$0.294067\pi$
$644$			214.833i			0.333592i
$645$	353.232	−	1523.71i	0.547647	−	2.36235i
$646$	230.865			0.357377
$647$	694.291	+	694.291i	1.07309	+	1.07309i	0.997109	+	0.0759830i	$0.0242095\pi$
$647$	694.291	+	694.291i	1.07309	+	1.07309i	0.0759830	+	0.997109i	$0.475791\pi$
$648$	184.700	−	184.700i	0.285030	−	0.285030i
$649$		−	839.742i		−	1.29390i
$650$	−296.900	−	145.475i	−0.456769	−	0.223807i
$651$	−8.32508			−0.0127881
$652$	−90.4499	−	90.4499i	−0.138727	−	0.138727i
$653$	187.784	−	187.784i	0.287571	−	0.287571i	−0.548548	−	0.836119i	$-0.684819\pi$
$653$	187.784	−	187.784i	0.287571	−	0.287571i	0.836119	+	0.548548i	$0.184819\pi$
$654$			889.190i			1.35962i
$655$	714.224	+	165.574i	1.09042	+	0.252784i
$656$	118.700			0.180945
$657$	−257.300	−	257.300i	−0.391629	−	0.391629i
$658$	239.575	−	239.575i	0.364095	−	0.364095i
$659$		−	144.983i		−	0.220004i	−0.993931	−	0.110002i	$-0.964914\pi$
$659$		−	144.983i		−	0.220004i	0.993931	−	0.110002i	$-0.0350858\pi$
$660$	−300.049	−	481.150i	−0.454620	−	0.729015i
$661$	−433.266			−0.655470			−0.327735	−	0.944770i	$-0.606285\pi$
$661$	−433.266			−0.655470			−0.327735	+	0.944770i	$0.606285\pi$
$662$	65.2831	+	65.2831i	0.0986149	+	0.0986149i
$663$	307.370	−	307.370i	0.463605	−	0.463605i
$664$		−	315.867i		−	0.475703i
$665$	160.049	−	99.8084i	0.240676	−	0.150088i
$666$	−557.132			−0.836535
$667$	575.124	+	575.124i	0.862254	+	0.862254i
$668$	156.075	−	156.075i	0.233646	−	0.233646i
$669$			648.399i			0.969207i
$670$	−94.1916	+	406.308i	−0.140584	+	0.606430i
$671$	1214.63			1.81018
$672$	−42.9666	−	42.9666i	−0.0639384	−	0.0639384i
$673$	−783.315	+	783.315i	−1.16392	+	1.16392i	−0.180305	+	0.983611i	$0.557709\pi$
$673$	−783.315	+	783.315i	−1.16392	+	1.16392i	−0.983611	+	0.180305i	$0.942291\pi$
$674$			36.0172i			0.0534380i
$675$	49.8547	+	145.646i	0.0738588	+	0.215772i
$676$	−163.100			−0.241272
$677$	232.380	+	232.380i	0.343250	+	0.343250i	0.857588	−	0.514338i	$-0.171962\pi$
$677$	232.380	+	232.380i	0.343250	+	0.343250i	−0.514338	+	0.857588i	$0.671962\pi$
$678$	−568.566	+	568.566i	−0.838593	+	0.838593i
$679$			211.575i			0.311598i
$680$	157.733	+	36.5662i	0.231960	+	0.0537738i
$681$	492.516			0.723224
$682$	10.8245	+	10.8245i	0.0158717	+	0.0158717i
$683$	18.6997	−	18.6997i	0.0273787	−	0.0273787i	−0.693285	−	0.720664i	$-0.743837\pi$
$683$	18.6997	−	18.6997i	0.0273787	−	0.0273787i	0.720664	+	0.693285i	$0.243837\pi$
$684$			213.399i			0.311987i
$685$	−27.5006	−	44.0990i	−0.0401468	−	0.0643781i
$686$	−26.1916			−0.0381802
$687$	619.741	+	619.741i	0.902097	+	0.902097i
$688$	−217.933	+	217.933i	−0.316763	+	0.316763i
$689$			234.192i			0.339901i
$690$	988.999	−	616.749i	1.43333	−	0.893839i
$691$	−736.598			−1.06599			−0.532995	−	0.846119i	$-0.678933\pi$
$691$	−736.598			−1.06599			−0.532995	+	0.846119i	$0.678933\pi$
$692$	−204.174	−	204.174i	−0.295050	−	0.295050i
$693$	195.533	−	195.533i	0.282154	−	0.282154i
$694$		−	275.251i		−	0.396615i
$695$	−60.8245	+	262.375i	−0.0875173	+	0.377517i
$696$	−230.049			−0.330531
$697$	−240.242	−	240.242i	−0.344680	−	0.344680i
$698$	496.174	−	496.174i	0.710852	−	0.710852i
$699$			445.266i			0.637004i
$700$	125.158	−	42.8418i	0.178797	−	0.0612025i
$701$	518.483			0.739634			0.369817	−	0.929105i	$-0.379420\pi$
$701$	518.483			0.739634			0.369817	+	0.929105i	$0.379420\pi$
$702$	−57.5834	−	57.5834i	−0.0820277	−	0.0820277i
$703$	−530.766	+	530.766i	−0.755002	+	0.755002i
$704$			111.733i			0.158712i
$705$	−1790.68	−	415.121i	−2.53997	−	0.588823i
$706$	−184.325			−0.261084
$707$	143.258	+	143.258i	0.202628	+	0.202628i
$708$	−345.216	+	345.216i	−0.487594	+	0.487594i
$709$		−	758.765i		−	1.07019i	−0.844792	−	0.535095i	$-0.820276\pi$
$709$		−	758.765i		−	1.07019i	0.844792	−	0.535095i	$-0.179724\pi$
$710$	177.666	+	284.900i	0.250234	+	0.401267i
$711$	−68.3487			−0.0961304
$712$	160.000	+	160.000i	0.224719	+	0.224719i
$713$	−22.2497	+	22.2497i	−0.0312058	+	0.0312058i
$714$			173.925i			0.243592i
$715$	−554.125	+	345.558i	−0.775000	+	0.483297i
$716$	−496.499			−0.693435
$717$	−87.4629	−	87.4629i	−0.121984	−	0.121984i
$718$	−592.232	+	592.232i	−0.824836	+	0.824836i
$719$		−	16.7341i		−	0.0232742i	−0.999932	−	0.0116371i	$-0.996296\pi$
$719$		−	16.7341i		−	0.0232742i	0.999932	−	0.0116371i	$-0.00370429\pi$
$720$	−33.7998	+	145.800i	−0.0469441	+	0.202500i
$721$	−211.575			−0.293446
$722$	−157.700	−	157.700i	−0.218421	−	0.218421i
$723$	115.791	−	115.791i	0.160154	−	0.160154i
$724$		−	34.3165i		−	0.0473984i
$725$	220.367	−	449.748i	0.303955	−	0.620342i
$726$	−425.266			−0.585766
$727$	34.7836	+	34.7836i	0.0478455	+	0.0478455i	0.730625	−	0.682779i	$-0.239229\pi$
$727$	34.7836	+	34.7836i	0.0478455	+	0.0478455i	−0.682779	+	0.730625i	$0.739229\pi$
$728$	−49.4833	+	49.4833i	−0.0679716	+	0.0679716i
$729$		−	466.083i		−	0.639345i
$730$	−334.949	−	77.6491i	−0.458835	−	0.106369i
$731$	882.172			1.20680
$732$	−499.333	−	499.333i	−0.682148	−	0.682148i
$733$	−754.703	+	754.703i	−1.02961	+	1.02961i	−0.0300602	+	0.999548i	$0.509570\pi$
$733$	−754.703	+	754.703i	−1.02961	+	1.02961i	−0.999548	+	0.0300602i	$0.990430\pi$
$734$		−	84.1744i		−	0.114679i
$735$	75.1916	+	120.575i	0.102301	+	0.164047i
$736$	−229.666			−0.312047
$737$	582.524	+	582.524i	0.790399	+	0.790399i
$738$	222.067	−	222.067i	0.300903	−	0.300903i
$739$		−	303.549i		−	0.410756i	−0.978683	−	0.205378i	$-0.934158\pi$
$739$		−	303.549i		−	0.410756i	0.978683	−	0.205378i	$-0.0658424\pi$
$740$	−446.700	+	278.566i	−0.603648	+	0.376441i
$741$	541.341			0.730555
$742$	−66.2583	−	66.2583i	−0.0892970	−	0.0892970i
$743$	549.424	−	549.424i	0.739467	−	0.739467i	−0.233008	−	0.972475i	$-0.574857\pi$
$743$	549.424	−	549.424i	0.739467	−	0.739467i	0.972475	+	0.233008i	$0.0748568\pi$
$744$		−	8.89989i		−	0.0119622i
$745$	95.5845	−	412.316i	0.128301	−	0.553445i
$746$	320.267			0.429312
$747$	−590.932	−	590.932i	−0.791074	−	0.791074i
$748$	226.142	−	226.142i	0.302329	−	0.302329i
$749$			102.459i			0.136794i
$750$	−556.533	−	453.183i	−0.742044	−	0.604244i
$751$	4.50056			0.00599275			0.00299638	−	0.999996i	$-0.499046\pi$
$751$	4.50056			0.00599275			0.00299638	+	0.999996i	$0.499046\pi$
$752$	256.116	+	256.116i	0.340580	+	0.340580i
$753$	−273.208	+	273.208i	−0.362826	+	0.362826i
$754$			264.941i			0.351380i
$755$	−106.346	−	24.6534i	−0.140855	−	0.0326535i
$756$	32.5834			0.0430998
$757$	−342.532	−	342.532i	−0.452486	−	0.452486i	0.443693	−	0.896179i	$-0.353668\pi$
$757$	−342.532	−	342.532i	−0.452486	−	0.452486i	−0.896179	+	0.443693i	$0.853668\pi$
$758$	749.066	−	749.066i	0.988213	−	0.988213i
$759$		−	2302.16i		−	3.03315i
$760$	106.700	+	171.100i	0.140394	+	0.225132i
$761$	−198.267			−0.260535			−0.130267	−	0.991479i	$-0.541584\pi$
$761$	−198.267			−0.260535			−0.130267	+	0.991479i	$0.541584\pi$
$762$	−369.141	−	369.141i	−0.484437	−	0.484437i
$763$	−289.729	+	289.729i	−0.379723	+	0.379723i
$764$			401.832i			0.525958i
$765$	363.501	−	226.682i	0.475164	−	0.296317i
$766$	590.799			0.771278
$767$	397.575	+	397.575i	0.518350	+	0.518350i
$768$	45.9333	−	45.9333i	0.0598089	−	0.0598089i
$769$		−	423.158i		−	0.550271i	−0.961405	−	0.275135i	$-0.911277\pi$
$769$		−	423.158i		−	0.550271i	0.961405	−	0.275135i	$-0.0887227\pi$
$770$	59.0086	−	254.541i	0.0766346	−	0.330573i
$771$	1553.50			2.01491
$772$	243.600	+	243.600i	0.315543	+	0.315543i
$773$	893.620	−	893.620i	1.15604	−	1.15604i	0.170722	−	0.985319i	$-0.445390\pi$
$773$	893.620	−	893.620i	1.15604	−	1.15604i	0.985319	−	0.170722i	$-0.0546101\pi$
$774$			815.432i			1.05353i
$775$	17.3993	+	8.52531i	0.0224508	+	0.0110004i
$776$	−226.183			−0.291473
$777$	−399.858	−	399.858i	−0.514618	−	0.514618i
$778$	387.116	−	387.116i	0.497579	−	0.497579i
$779$		−	423.115i		−	0.543152i
$780$	369.858	+	85.7417i	0.474177	+	0.109925i
$781$	663.182			0.849145
$782$	464.833	+	464.833i	0.594416	+	0.594416i
$783$	87.2282	−	87.2282i	0.111403	−	0.111403i
$784$		−	28.0000i		−	0.0357143i
$785$	130.334	+	208.999i	0.166030	+	0.266241i
$786$	−841.916			−1.07114
$787$	−820.137	−	820.137i	−1.04211	−	1.04211i	−0.999074	−	0.0430313i	$-0.986298\pi$
$787$	−820.137	−	820.137i	−1.04211	−	1.04211i	−0.0430313	−	0.999074i	$-0.513702\pi$
$788$	430.250	−	430.250i	0.546002	−	0.546002i
$789$		−	1056.27i		−	1.33875i
$790$	−54.8009	+	34.1744i	−0.0693682	+	0.0432587i
$791$	−370.517			−0.468416
$792$	209.033	+	209.033i	0.263931	+	0.263931i
$793$	−575.066	+	575.066i	−0.725177	+	0.725177i
$794$			564.407i			0.710840i
$795$	−114.808	+	495.241i	−0.144413	+	0.622945i
$796$	186.583			0.234401
$797$	−300.653	−	300.653i	−0.377231	−	0.377231i	0.492871	−	0.870102i	$-0.335947\pi$
$797$	−300.653	−	300.653i	−0.377231	−	0.377231i	−0.870102	+	0.492871i	$0.835947\pi$
$798$	−153.158	+	153.158i	−0.191928	+	0.191928i
$799$		−	1036.73i		−	1.29754i
$800$	45.7998	+	133.800i	0.0572497	+	0.167250i
$801$	598.665			0.747397
$802$	95.6502	+	95.6502i	0.119265	+	0.119265i
$803$	−480.217	+	480.217i	−0.598029	+	0.598029i
$804$		−	478.949i		−	0.595708i
$805$	523.208	+	121.292i	0.649947	+	0.150673i
$806$	−10.2497			−0.0127168
$807$	64.5920	+	64.5920i	0.0800397	+	0.0800397i
$808$	−153.150	+	153.150i	−0.189542	+	0.189542i
$809$			1060.03i			1.31030i	0.755498	+	0.655150i	$0.227395\pi$
$809$			1060.03i			1.31030i	−0.755498	+	0.655150i	$0.772605\pi$
$810$	−345.541	−	554.099i	−0.426594	−	0.684073i
$811$	726.801			0.896179			0.448089	−	0.893989i	$-0.352105\pi$
$811$	726.801			0.896179			0.448089	+	0.893989i	$0.352105\pi$
$812$	−74.9580	−	74.9580i	−0.0923128	−	0.0923128i
$813$	−442.299	+	442.299i	−0.544033	+	0.544033i
$814$			1039.81i			1.27741i
$815$	−271.350	+	169.216i	−0.332945	+	0.207627i
$816$	−185.933			−0.227859
$817$	776.842	+	776.842i	0.950847	+	0.950847i
$818$	−113.875	+	113.875i	−0.139212	+	0.139212i
$819$			185.150i			0.226068i
$820$	67.0161	−	289.083i	0.0817270	−	0.352540i
$821$	775.314			0.944354			0.472177	−	0.881504i	$-0.343468\pi$
$821$	775.314			0.944354			0.472177	+	0.881504i	$0.343468\pi$
$822$	42.2002	+	42.2002i	0.0513385	+	0.0513385i
$823$	724.025	−	724.025i	0.879738	−	0.879738i	−0.113769	−	0.993507i	$-0.536292\pi$
$823$	724.025	−	724.025i	0.879738	−	0.879738i	0.993507	+	0.113769i	$0.0362923\pi$
$824$		−	226.183i		−	0.274494i
$825$	−1341.20	+	459.095i	−1.62570	+	0.556478i
$826$	−224.967			−0.272357
$827$	301.457	+	301.457i	0.364519	+	0.364519i	0.865474	−	0.500954i	$-0.167018\pi$
$827$	301.457	+	301.457i	0.364519	+	0.364519i	−0.500954	+	0.865474i	$0.667018\pi$
$828$	−429.666	+	429.666i	−0.518921	+	0.518921i
$829$			126.325i			0.152382i	0.997093	+	0.0761912i	$0.0242760\pi$
$829$			126.325i			0.152382i	−0.997093	+	0.0761912i	$0.975724\pi$
$830$	−769.266	−	178.334i	−0.926826	−	0.214860i
$831$	1929.43			2.32182
$832$	−52.8999	−	52.8999i	−0.0635816	−	0.0635816i
$833$	−56.6706	+	56.6706i	−0.0680319	+	0.0680319i
$834$		−	309.283i		−	0.370843i
$835$	−291.990	−	468.226i	−0.349689	−	0.560750i
$836$	398.282			0.476414
$837$	3.37458	+	3.37458i	0.00403176	+	0.00403176i
$838$	−445.158	+	445.158i	−0.531215	+	0.531215i
$839$		−	176.166i		−	0.209971i	−0.994474	−	0.104986i	$-0.966520\pi$
$839$		−	176.166i		−	0.209971i	0.994474	−	0.104986i	$-0.0334796\pi$
$840$	−128.900	+	80.3832i	−0.153452	+	0.0956943i
$841$	439.664			0.522787
$842$	−164.333	−	164.333i	−0.195169	−	0.195169i
$843$	813.304	−	813.304i	0.964773	−	0.964773i
$844$		−	148.700i		−	0.176184i
$845$	−92.0840	+	397.216i	−0.108975	+	0.470079i
$846$	958.299			1.13274
$847$	−138.566	−	138.566i	−0.163596	−	0.163596i
$848$	70.8331	−	70.8331i	0.0835297	−	0.0835297i
$849$			1109.98i			1.30740i
$850$	178.108	−	363.501i	0.209538	−	0.427648i
$851$	−2137.33			−2.51155
$852$	−272.633	−	272.633i	−0.319992	−	0.319992i
$853$	−221.234	+	221.234i	−0.259359	+	0.259359i	−0.824793	−	0.565434i	$-0.808709\pi$
$853$	−221.234	+	221.234i	−0.259359	+	0.259359i	0.565434	+	0.824793i	$0.308709\pi$
$854$		−	325.399i		−	0.381030i
$855$	519.716	+	120.482i	0.607855	+	0.140915i
$856$	−109.533			−0.127959
$857$	−777.533	−	777.533i	−0.907273	−	0.907273i	0.0887786	−	0.996051i	$-0.471704\pi$
$857$	−777.533	−	777.533i	−0.907273	−	0.907273i	−0.996051	+	0.0887786i	$0.971704\pi$
$858$	530.266	−	530.266i	0.618025	−	0.618025i
$859$		−	62.7987i		−	0.0731067i	−0.999332	−	0.0365534i	$-0.988362\pi$
$859$		−	62.7987i		−	0.0731067i	0.999332	−	0.0365534i	$-0.0116379\pi$
$860$	407.716	+	653.800i	0.474088	+	0.760232i
$861$	318.758			0.370218
$862$	−466.199	−	466.199i	−0.540834	−	0.540834i
$863$	−681.874	+	681.874i	−0.790121	+	0.790121i	−0.981513	−	0.191393i	$-0.938700\pi$
$863$	−681.874	+	681.874i	−0.790121	+	0.790121i	0.191393	+	0.981513i	$0.438700\pi$
$864$			34.8331i			0.0403161i
$865$	−612.523	+	381.975i	−0.708119	+	0.441590i
$866$	−442.549			−0.511026
$867$	−453.350	−	453.350i	−0.522895	−	0.522895i
$868$	2.89989	−	2.89989i	0.00334089	−	0.00334089i
$869$			127.564i			0.146794i
$870$	−129.883	+	560.266i	−0.149290	+	0.643984i
$871$	−551.591			−0.633285
$872$	−309.733	−	309.733i	−0.355198	−	0.355198i
$873$	−423.150	+	423.150i	−0.484707	+	0.484707i
$874$			818.665i			0.936688i
$875$	−33.6749	−	329.000i	−0.0384856	−	0.376000i
$876$	394.833			0.450723
$877$	−1019.15	−	1019.15i	−1.16208	−	1.16208i	−0.984018	−	0.178066i	$-0.943016\pi$
$877$	−1019.15	−	1019.15i	−1.16208	−	1.16208i	−0.178066	−	0.984018i	$-0.556984\pi$
$878$	32.5662	−	32.5662i	0.0370913	−	0.0370913i
$879$			1988.98i			2.26278i
$880$	272.116	+	63.0829i	0.309223	+	0.0716851i
$881$	−77.5673			−0.0880446			−0.0440223	−	0.999031i	$-0.514017\pi$
$881$	−77.5673			−0.0880446			−0.0440223	+	0.999031i	$0.514017\pi$
$882$	−52.3832	−	52.3832i	−0.0593914	−	0.0593914i
$883$	954.566	−	954.566i	1.08105	−	1.08105i	0.0846371	−	0.996412i	$-0.473027\pi$
$883$	954.566	−	954.566i	1.08105	−	1.08105i	0.996412	−	0.0846371i	$-0.0269731\pi$
$884$			214.133i			0.242232i
$885$	645.841	+	1035.65i	0.729763	+	1.17022i
$886$	−625.699			−0.706206
$887$	307.150	+	307.150i	0.346279	+	0.346279i	0.858722	−	0.512442i	$-0.171259\pi$
$887$	307.150	+	307.150i	0.346279	+	0.346279i	−0.512442	+	0.858722i	$0.671259\pi$
$888$	427.466	−	427.466i	0.481381	−	0.481381i
$889$		−	240.558i		−	0.270593i
$890$	480.000	−	299.333i	0.539326	−	0.336329i
$891$	−1289.82			−1.44760
$892$	−225.858	−	225.858i	−0.253204	−	0.253204i
$893$	912.948	−	912.948i	1.02234	−	1.02234i
$894$			486.032i			0.543660i
$895$	−280.316	+	1209.18i	−0.313203	+	1.35104i
$896$	29.9333			0.0334077
$897$	1089.96	+	1089.96i	1.21511	+	1.21511i
$898$	276.582	−	276.582i	0.307998	−	0.307998i
$899$		−	15.5264i		−	0.0172708i
$900$	336.000	+	164.633i	0.373333	+	0.182925i
$901$	−286.726			−0.318230
$902$	−414.459	−	414.459i	−0.459488	−	0.459488i
$903$	−585.241	+	585.241i	−0.648108	+	0.648108i
$904$		−	396.099i		−	0.438163i
$905$	−83.5748	−	19.3746i	−0.0923479	−	0.0214084i
$906$	125.358			0.138365
$907$	−608.192	−	608.192i	−0.670553	−	0.670553i	0.287290	−	0.957844i	$-0.407246\pi$
$907$	−608.192	−	608.192i	−0.670553	−	0.670553i	−0.957844	+	0.287290i	$0.907246\pi$
$908$	−171.559	+	171.559i	−0.188941	+	0.188941i
$909$			573.033i			0.630400i
$910$	92.5748	+	148.450i	0.101731	+	0.163132i
$911$	1336.46			1.46703			0.733515	−	0.679673i	$-0.237878\pi$
$911$	1336.46			1.46703			0.733515	+	0.679673i	$0.237878\pi$
$912$	−163.733	−	163.733i	−0.179532	−	0.179532i
$913$	−1102.90	+	1102.90i	−1.20799	+	1.20799i
$914$		−	154.883i		−	0.169456i
$915$	−1498.00	+	934.166i	−1.63716	+	1.02095i
$916$	−431.750			−0.471343
$917$	−274.325	−	274.325i	−0.299155	−	0.299155i
$918$	70.5006	−	70.5006i	0.0767980	−	0.0767980i
$919$		−	358.632i		−	0.390241i	−0.980779	−	0.195121i	$-0.937490\pi$
$919$		−	358.632i		−	0.390241i	0.980779	−	0.195121i	$-0.0625099\pi$
$920$	−129.666	+	559.333i	−0.140942	+	0.607970i
$921$	1409.65			1.53056
$922$	615.600	+	615.600i	0.667678	+	0.667678i
$923$	−313.983	+	313.983i	−0.340176	+	0.340176i
$924$			300.049i			0.324729i
$925$	426.224	+	1245.17i	0.460783	+	1.34613i
$926$	−293.132			−0.316558
$927$	−423.150	−	423.150i	−0.456472	−	0.456472i
$928$	80.1335	−	80.1335i	0.0863507	−	0.0863507i
$929$			399.023i			0.429518i	0.976667	+	0.214759i	$0.0688967\pi$
$929$			399.023i			0.429518i	−0.976667	+	0.214759i	$0.931103\pi$
$930$	−21.6749	−	5.02475i	−0.0233064	−	0.00540296i
$931$	−99.8084			−0.107206
$932$	−155.100	−	155.100i	−0.166416	−	0.166416i
$933$	933.282	−	933.282i	1.00030	−	1.00030i
$934$			190.142i			0.203578i
$935$	−423.073	−	678.426i	−0.452485	−	0.725590i
$936$	−197.933			−0.211467
$937$	149.237	+	149.237i	0.159271	+	0.159271i	0.782244	−	0.622973i	$-0.214075\pi$
$937$	149.237	+	149.237i	0.159271	+	0.159271i	−0.622973	+	0.782244i	$0.714075\pi$
$938$	156.058	−	156.058i	0.166373	−	0.166373i
$939$		−	1309.17i		−	1.39421i
$940$	768.349	−	479.150i	0.817392	−	0.509734i
$941$	−719.397			−0.764503			−0.382251	−	0.924058i	$-0.624851\pi$
$941$	−719.397			−0.764503			−0.382251	+	0.924058i	$0.624851\pi$
$942$	−200.000	−	200.000i	−0.212314	−	0.212314i
$943$	851.916	−	851.916i	0.903410	−	0.903410i
$944$		−	240.499i		−	0.254766i
$945$	18.3961	−	79.3541i	0.0194668	−	0.0839726i
$946$	1521.90			1.60877
$947$	−35.9408	−	35.9408i	−0.0379522	−	0.0379522i	0.687876	−	0.725828i	$-0.258543\pi$
$947$	−35.9408	−	35.9408i	−0.0379522	−	0.0379522i	−0.725828	+	0.687876i	$0.758543\pi$
$948$	52.4413	−	52.4413i	0.0553179	−	0.0553179i
$949$		−	454.717i		−	0.479154i
$950$	476.941	−	163.257i	0.502043	−	0.171850i
$951$	−1807.47			−1.90060
$952$	−60.5834	−	60.5834i	−0.0636381	−	0.0636381i
$953$	178.057	−	178.057i	0.186838	−	0.186838i	−0.607489	−	0.794328i	$-0.707823\pi$
$953$	178.057	−	178.057i	0.186838	−	0.186838i	0.794328	+	0.607489i	$0.207823\pi$
$954$		−	265.033i		−	0.277813i
$955$	978.628	+	226.869i	1.02474	+	0.237559i
$956$	60.9321			0.0637366
$957$	803.254	+	803.254i	0.839346	+	0.839346i
$958$	32.0667	−	32.0667i	0.0334726	−	0.0334726i
$959$			27.5006i			0.0286763i
$960$	−85.9333	−	137.800i	−0.0895138	−	0.143541i
$961$	−960.399			−0.999375
$962$	−492.299	−	492.299i	−0.511746	−	0.511746i
$963$	−204.917	+	204.917i	−0.212790	+	0.212790i
$964$			80.6674i			0.0836799i
$965$	730.799	−	455.733i	0.757304	−	0.472262i
$966$	−616.749			−0.638457
$967$	−288.417	−	288.417i	−0.298259	−	0.298259i	0.542073	−	0.840332i	$-0.317640\pi$
$967$	−288.417	−	288.417i	−0.298259	−	0.298259i	−0.840332	+	0.542073i	$0.817640\pi$
$968$	148.133	−	148.133i	0.153030	−	0.153030i
$969$			662.775i			0.683978i
$970$	−127.700	+	550.849i	−0.131649	+	0.567886i
$971$	−212.474			−0.218819			−0.109410	−	0.993997i	$-0.534896\pi$
$971$	−212.474			−0.218819			−0.109410	+	0.993997i	$0.534896\pi$
$972$	451.867	+	451.867i	0.464883	+	0.464883i
$973$	100.775	−	100.775i	0.103571	−	0.103571i
$974$			898.648i			0.922636i
$975$	417.633	−	852.349i	0.428341	−	0.874204i
$976$	347.867			0.356421
$977$	53.5662	+	53.5662i	0.0548272	+	0.0548272i	0.733989	−	0.679162i	$-0.237656\pi$
$977$	53.5662	+	53.5662i	0.0548272	+	0.0548272i	−0.679162	+	0.733989i	$0.737656\pi$
$978$	259.666	−	259.666i	0.265507	−	0.265507i
$979$		−	1117.33i		−	1.14130i
$980$	−68.1916	−	15.8084i	−0.0695833	−	0.0161310i
$981$	−1158.91			−1.18136
$982$	−322.216	−	322.216i	−0.328123	−	0.328123i
$983$	612.070	−	612.070i	0.622655	−	0.622655i	−0.323554	−	0.946210i	$-0.604878\pi$
$983$	612.070	−	612.070i	0.622655	−	0.622655i	0.946210	+	0.323554i	$0.104878\pi$
$984$			340.766i			0.346307i
$985$	−804.924	−	1290.75i	−0.817181	−	1.31041i
$986$	−324.372			−0.328978
$987$	687.778	+	687.778i	0.696837	+	0.696837i
$988$	−188.566	+	188.566i	−0.190856	+	0.190856i
$989$			3128.25i			3.16304i
$990$	627.100	−	391.066i	0.633434	−	0.395016i
$991$	−699.666			−0.706020			−0.353010	−	0.935619i	$-0.614842\pi$
$991$	−699.666			−0.706020			−0.353010	+	0.935619i	$0.614842\pi$
$992$	3.10011	+	3.10011i	0.00312511	+	0.00312511i
$993$	−187.417	+	187.417i	−0.188738	+	0.188738i
$994$		−	177.666i		−	0.178739i
$995$	105.342	−	454.408i	0.105872	−	0.456691i
$996$	906.799			0.910440
$997$	682.529	+	682.529i	0.684582	+	0.684582i	0.961029	−	0.276447i	$-0.0891570\pi$
$997$	682.529	+	682.529i	0.684582	+	0.684582i	−0.276447	+	0.961029i	$0.589157\pi$
$998$	925.648	−	925.648i	0.927503	−	0.927503i
$999$			324.166i			0.324490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.3.f.a.57.2	yes	4
3.2	odd	2		630.3.o.a.127.1		4
4.3	odd	2		560.3.bh.b.337.1		4
5.2	odd	4		350.3.f.b.43.1		4
5.3	odd	4	inner	70.3.f.a.43.2	✓	4
5.4	even	2		350.3.f.b.57.1		4
7.6	odd	2		490.3.f.d.197.1		4
15.8	even	4		630.3.o.a.253.1		4
20.3	even	4		560.3.bh.b.113.1		4
35.13	even	4		490.3.f.d.393.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.f.a.43.2	✓	4	5.3	odd	4	inner
70.3.f.a.57.2	yes	4	1.1	even	1	trivial
350.3.f.b.43.1		4	5.2	odd	4
350.3.f.b.57.1		4	5.4	even	2
490.3.f.d.197.1		4	7.6	odd	2
490.3.f.d.393.1		4	35.13	even	4
560.3.bh.b.113.1		4	20.3	even	4
560.3.bh.b.337.1		4	4.3	odd	2
630.3.o.a.127.1		4	3.2	odd	2
630.3.o.a.253.1		4	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	70.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(2.87083 - 2.87083i) q^{3} +2.00000i q^{4} +(4.87083 + 1.12917i) q^{5} -5.74166 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -7.48331i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(2.87083 - 2.87083i) q^{3} +2.00000i q^{4} +(4.87083 + 1.12917i) q^{5} -5.74166 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -7.48331i q^{9} +(-3.74166 - 6.00000i) q^{10} -13.9666 q^{11} +(5.74166 + 5.74166i) q^{12} +(6.61249 - 6.61249i) q^{13} +3.74166i q^{14} +(17.2250 - 10.7417i) q^{15} -4.00000 q^{16} +(8.09580 + 8.09580i) q^{17} +(-7.48331 + 7.48331i) q^{18} +14.2583i q^{19} +(-2.25834 + 9.74166i) q^{20} -10.7417 q^{21} +(13.9666 + 13.9666i) q^{22} +(-28.7083 + 28.7083i) q^{23} -11.4833i q^{24} +(22.4499 + 11.0000i) q^{25} -13.2250 q^{26} +(4.35414 + 4.35414i) q^{27} +(3.74166 - 3.74166i) q^{28} -20.0334i q^{29} +(-27.9666 - 6.48331i) q^{30} +0.775028 q^{31} +(4.00000 + 4.00000i) q^{32} +(-40.0958 + 40.0958i) q^{33} -16.1916i q^{34} +(-7.00000 - 11.2250i) q^{35} +14.9666 q^{36} +(37.2250 + 37.2250i) q^{37} +(14.2583 - 14.2583i) q^{38} -37.9666i q^{39} +(12.0000 - 7.48331i) q^{40} -29.6749 q^{41} +(10.7417 + 10.7417i) q^{42} +(54.4833 - 54.4833i) q^{43} -27.9333i q^{44} +(8.44994 - 36.4499i) q^{45} +57.4166 q^{46} +(-64.0291 - 64.0291i) q^{47} +(-11.4833 + 11.4833i) q^{48} +7.00000i q^{49} +(-11.4499 - 33.4499i) q^{50} +46.4833 q^{51} +(13.2250 + 13.2250i) q^{52} +(-17.7083 + 17.7083i) q^{53} -8.70829i q^{54} +(-68.0291 - 15.7707i) q^{55} -7.48331 q^{56} +(40.9333 + 40.9333i) q^{57} +(-20.0334 + 20.0334i) q^{58} +60.1249i q^{59} +(21.4833 + 34.4499i) q^{60} -86.9666 q^{61} +(-0.775028 - 0.775028i) q^{62} +(-14.0000 + 14.0000i) q^{63} -8.00000i q^{64} +(39.6749 - 24.7417i) q^{65} +80.1916 q^{66} +(-41.7083 - 41.7083i) q^{67} +(-16.1916 + 16.1916i) q^{68} +164.833i q^{69} +(-4.22497 + 18.2250i) q^{70} -47.4833 q^{71} +(-14.9666 - 14.9666i) q^{72} +(34.3832 - 34.3832i) q^{73} -74.4499i q^{74} +(96.0291 - 32.8708i) q^{75} -28.5167 q^{76} +(26.1292 + 26.1292i) q^{77} +(-37.9666 + 37.9666i) q^{78} -9.13348i q^{79} +(-19.4833 - 4.51669i) q^{80} +92.3498 q^{81} +(29.6749 + 29.6749i) q^{82} +(78.9666 - 78.9666i) q^{83} -21.4833i q^{84} +(30.2917 + 48.5748i) q^{85} -108.967 q^{86} +(-57.5124 - 57.5124i) q^{87} +(-27.9333 + 27.9333i) q^{88} +80.0000i q^{89} +(-44.8999 + 28.0000i) q^{90} -24.7417 q^{91} +(-57.4166 - 57.4166i) q^{92} +(2.22497 - 2.22497i) q^{93} +128.058i q^{94} +(-16.1001 + 69.4499i) q^{95} +22.9666 q^{96} +(-56.5457 - 56.5457i) q^{97} +(7.00000 - 7.00000i) q^{98} +104.517i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 12 q^{5} - 8 q^{6} + 8 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 12 * q^5 - 8 * q^6 + 8 * q^8	\( 4 q - 4 q^{2} + 4 q^{3} + 12 q^{5} - 8 q^{6} + 8 q^{8} + 4 q^{11} + 8 q^{12} + 4 q^{13} + 24 q^{15} - 16 q^{16} - 20 q^{17} - 24 q^{20} - 28 q^{21} - 4 q^{22} - 40 q^{23} - 8 q^{26} - 20 q^{27} - 52 q^{30} + 48 q^{31} + 16 q^{32} - 108 q^{33} - 28 q^{35} + 104 q^{37} + 72 q^{38} + 48 q^{40} + 16 q^{41} + 28 q^{42} + 188 q^{43} - 56 q^{45} + 80 q^{46} - 84 q^{47} - 16 q^{48} + 44 q^{50} + 156 q^{51} + 8 q^{52} + 4 q^{53} - 100 q^{55} + 44 q^{57} - 140 q^{58} + 56 q^{60} - 288 q^{61} - 48 q^{62} - 56 q^{63} + 24 q^{65} + 216 q^{66} - 92 q^{67} + 40 q^{68} + 28 q^{70} - 160 q^{71} - 72 q^{73} + 212 q^{75} - 144 q^{76} + 112 q^{77} - 92 q^{78} - 48 q^{80} + 100 q^{81} - 16 q^{82} + 256 q^{83} + 196 q^{85} - 376 q^{86} - 28 q^{87} + 8 q^{88} - 84 q^{91} - 80 q^{92} - 36 q^{93} - 244 q^{95} + 32 q^{96} - 84 q^{97} + 28 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 12 * q^5 - 8 * q^6 + 8 * q^8 + 4 * q^11 + 8 * q^12 + 4 * q^13 + 24 * q^15 - 16 * q^16 - 20 * q^17 - 24 * q^20 - 28 * q^21 - 4 * q^22 - 40 * q^23 - 8 * q^26 - 20 * q^27 - 52 * q^30 + 48 * q^31 + 16 * q^32 - 108 * q^33 - 28 * q^35 + 104 * q^37 + 72 * q^38 + 48 * q^40 + 16 * q^41 + 28 * q^42 + 188 * q^43 - 56 * q^45 + 80 * q^46 - 84 * q^47 - 16 * q^48 + 44 * q^50 + 156 * q^51 + 8 * q^52 + 4 * q^53 - 100 * q^55 + 44 * q^57 - 140 * q^58 + 56 * q^60 - 288 * q^61 - 48 * q^62 - 56 * q^63 + 24 * q^65 + 216 * q^66 - 92 * q^67 + 40 * q^68 + 28 * q^70 - 160 * q^71 - 72 * q^73 + 212 * q^75 - 144 * q^76 + 112 * q^77 - 92 * q^78 - 48 * q^80 + 100 * q^81 - 16 * q^82 + 256 * q^83 + 196 * q^85 - 376 * q^86 - 28 * q^87 + 8 * q^88 - 84 * q^91 - 80 * q^92 - 36 * q^93 - 244 * q^95 + 32 * q^96 - 84 * q^97 + 28 * q^98

Introduction

L-functions

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